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advance directive
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legal document that lists the patient’s wishes regarding life-sustaining medical treatments
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age of majority
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defined by each U.S. state as the age at which one can make their own decisions, including health-care decisions
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alternative substance
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nonregulated herbal substance or homeopathic medication
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chief complaint
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statement of the signs and symptoms that have led the patient to seek medical attention
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collaborative problem
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a certain physiological response the nurse monitors that can be addressed through nursing intervention and physician-prescribed treatments
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demographic data
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identifying basic patient information
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electronic health record (EHR)
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digital format of a patient’s chart that contains data related to the patient’s medical history, diagnoses, medications, treatment plans, immunization dates, allergies, radiology images, and laboratory and test results
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electronic medical record (EMR)
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single facility’s digital version of a patient’s chart
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familial disease
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disease that tends to occur often in particular families
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health information exchange (HIE)
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vehicle for doctors, nurses, patients, and other interdisciplinary healthcare members to access and securely share critical healthcare information electronically, improving the speed, quality, safety, and cost of patient care
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Health Information Technology for Economic and Clinical Health (HITECH) Act
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a law that promotes meaningful ways to incorporate health information technology while still protecting patients’ privacy rights
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Health Insurance Portability and Accountability Act(HIPAA)
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law that details national standards for electronic healthcare transactions and protection of privacy for health information
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health record
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collection of subjective and clinical information pertaining to a patient’s physical and mental health, compiled from a variety of sources
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healthcare informatics
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field that incorporates health care and computer and information sciences
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hereditary disease
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disease passed down from generation to generation
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initial health assessment
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systematic and purposeful collection and analysis of patient information
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interoperability
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the ability to share patient information across multiple healthcare systems in digital format
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meaningful use
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using electronic health information in a meaningful way to improve patient care
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medical power of attorney
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legal document that outlines who can make medical decisions on behalf of the patient in the event they cannot do so themselves
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minimum data set (MDS)
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standard established by healthcare institutions that specifies the information that must be collected from every patient
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nursing diagnosis
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clinical judgment based on the medical diagnosis of a patient that helps the nurse determine the plan of care
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objective data (also, signs)
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information observed through your senses of hearing, sight, smell, and touch while assessing the patient
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over-the-counter medication
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medication that does not require a prescription
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Patient Care Partnership
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document that tells the patient what to expect while receiving medical care under the organization and outlines their rights; formerly called a Patient Bill of Rights
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physical finding
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the assessment of a body system
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primary source
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the patient
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secondary source
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information obtained from the history section of the health record, or the patient’s family
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signs (also, objective data)
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information observed through your senses of hearing, sight, smell, and touch while assessing the patient
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subjective data (also, symptom)
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information obtained from the patient and/or family members and can provide important cues about functioning and unmet needs requiring assistance
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subpoena duces tecum
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court order to produce documents or records
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symptom (also, subjective data)
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information obtained from the patient and/or family members and can provide important cues about functioning and unmet needs requiring assistance
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treatment plan
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used to increase patient outcomes related to a specific disease or condition
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usability
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extent to which a product can be used by specified users to achieve specified goals with effectiveness, efficiency, and satisfaction in a specified context of use
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vital sign
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a marker of physiological homeostasis and essential in the analysis of monitoring patient progress; obtained by measuring body temperature, pulse, respiratory rate, and blood pressure


8.5: Status Offender
When we look at juvenile crime and detention, we must look at several issues surrounding the unique nature of the juvenile offender. First, we must differentiate between crimes and status offenses . Most times when a juvenile is arrested, it is thought they must have committed a crime. However, juveniles historically could be detained (incarcerated) for “status” offenses. These are “crimes” that only juveniles can be arrested for such as curfew violations, truancy or being “incorrigible,” basically not listening to your parent. These petty infractions could get a juvenile locked in a detention facility without even a hearing. Today, this no longer happens, and our guidelines have changed in regard to these offenses. However, it is important to know the history and the reason behind the practice. While status offenses are not serious, they are often precursor to more delinquent behavior.
Figure 8.5 Groundbreaking on Future Detention Home in Richmond Virginia, Dated June 14, 1956. Image is under a CC.By 2.0 license.
The Office of Juvenile Justice and Delinquency Prevention (OJJDP) recognized this as a significant issue pertaining to juvenile and provided research into the concern in the following abstract:
Scope of the Problem Status Offending behavior is often a sign of underlying personal, familial, community, and systemic issues, similar to the risk factors that underlie general offending. Sometimes these underlying issues contribute to delinquency later in life, putting youths at a higher risk for drug use, victimization, engagement in risky behavior, and overall increased potential for physical and mental health issues, including addiction (Greenwood and Turner 2011; Chuang and Wells 2010; Buffington, Dierkhising, and Marsh 2010; Henry, Knight, and Thornberry 2012; Mersky, Topitzes, and Reynolds 2012). Ample evidence supports the notion that less serious forms of delinquency often precede the onset of more serious delinquent acts (Huizinga, Loeber, and Thornberry 1995; Elliott, 1994). However, the “precursor to delinquency” view of status offending does not take into account the normal experimentation of childhood and adolescence or the diverse developmental pathways that can lead to serious delinquency (Kelley et al. 1997). Children and adolescents commonly experiment with behaviors that are not considered positive or prosocial, such as lying, being truant, or defying parents. Such experimentation allows youths to discover the negative consequences of their behaviors and learn from their mistakes. Most youths who engage in status and other minor offenses never progress to more serious behaviors (Kelley et al. 1997). States have formulated differing approaches to defining and handling status offenders. The approaches can be broadly divided into three categories: status offenders as delinquents, status offenders as neglected/abused dependents, or status offenders as a separate legislative category. The classification of offense behaviors largely dictates the kind of treatment and services that status offenders are likely to receive. The legal definition of a status offense is critical, as it can impact the treatment and availability of services to a youth in the juvenile justice system (Kendall 2007). Relatively few states define status offenses as delinquent behavior under statute, yet many status offenders end up being treated as de facto delinquents. One such way is through the use of probation as a disposition for status offenders, which is an option in 30 states (Szymanski 2006). Often, status offenders will be placed on probation, only to be later incarcerated as the result of a technical violation, regardless of whether the status offense was serious enough to initially warrant the use of confinement (Yeide and Cohen 2009).
Impact of Institutionalization : Research is limited with regard to the specific impacts of institutionalization on particular subgroups, such as status offenders. However, researchers have examined the general impact of institutionalization on juvenile offenders and consistently demonstrated that confinement in correctional facilities does not reduce reoffending and may increase it for certain youths (e.g., Lipsey and Cullen 2007). In some cases, status offenders are placed in the same facilities as juveniles who have committed more serious crimes, a practice that may increase deviant attitudes and behaviors among status offenders, such as the development of antisocial perspectives and gang affiliation (Levin and Cohen 2014). Juveniles experiencing confinement are eventually forced to navigate the barriers to reentry in the community, home, and school, which increases the chance of being rearrested and re-incarcerated (Levin and Cohen 2014). Further, research has shown that confinement fails to address underlying causes of status-offending behavior, and thus does not deter youths from committing future crimes (Hughes 2011; Holman and Ziedenberg 2006). Although most youths naturally “age out” of delinquency when social controls are enforced (Sweeten, Piquero, and Steinberg 2013; Tremblay et al. 2004), institutionalization can negate this type of development. When handled as delinquents and placed in juvenile facilities, status offenders may be put into environments that can lead to physical and emotional harm. Institutionalizing juveniles may negatively affect their social development by disrupting their social connectedness and support from family, school, and the community (Hughes 2011). Confinement in a secure environment can increase violent tendencies, exacerbate risk factors, and increase recidivism risk (Holman and Ziedenberg 2006). Studies done on juvenile delinquents show that community-based programming can be more effective than detention in preventing future crime (Hughes 2011; Holman and Ziedenberg 2006; Kendall 2007; Salsich and Trone 2013; Petitclerc et al. 2013). Although status offenders are noncriminal youths, they often possess many risk factors for future offending, which can be exacerbated by formal processing through the juvenile justice system. Research illustrates the need for immediate and efficacious community-based alternatives to help status-offending youths and their families. Strengthening of family relationships, social-control mechanisms, and other protective factors are integral in preventing future criminality among status offenders (Salsich and Trone 2013).
Conclusions - Currently, status-offense laws, terminology, and programs and practices vary widely across states (Hockenberry and Puzzanchera 2014). Some states choose to process juveniles formally through the system, with the idea that harsh treatment of young offenders will deter them from future criminal activity. Conversely, some research has shown that by further entangling young people and children in the juvenile justice system, they become more likely to be involved in a life of crime because of their increased exposure to other criminal peers, the justice system, and the effects of “labeling” (Petrosino et al. 2010). A meta-analysis by Petrosino and colleagues (2010) assessed 27 studies and found a small negative effect for formal system processing of juveniles, meaning that juveniles who were formally processed through the juvenile justice system were more likely to recidivate, compared with youths who were diverted from the system (although the difference was not statistically significant). As a result, more states are exploring alternative strategies to divert status offenders from the juvenile court process altogether (Coalition for Juvenile Justice 2012). Some resources have been developed for jurisdictions looking for specific information about options in the treatment of status-offending youths. For example, through its participation in the MacArthur Foundation’s Models for Change Resource Center Partnership, the Status Offense Reform Center (SORC) provides tools and techniques to improve the juvenile justice system in support of the equitable, rational, and effective treatment of status offenders. The SORC, operated by the Vera Institute of Justice (n.d.), serves as an information base for juvenile justice stakeholders and is available to provide information, guidance, and assistance to policymakers and practitioners who are interested in preventing the confinement of status offenders (Salsich and Trone 2013). Jurisdictions can make use of this information to consider options to the processing and treatment of status offenders and ensure that they are deinstitutionalized.


3.1: Quantum States of Multi-Particle Systems
So far, we have studied quantum mechanical systems consisting of single particles. The next important step is to look at systems of more than one particle. We shall see that the postulates of quantum mechanics, when applied to multi-particle systems, give rise to interesting and counterintuitive phenomena such as quantum entanglement .
Suppose we have two particles labeled \(A\) and \(B\) . If each individual particle is treated as a quantum system, the postulates of quantum mechanics require that its state be described by a vector in a Hilbert space. Let \(\mathscr{H}_A\) and \(\mathscr{H}_B\) denote the respective single-particle Hilbert spaces. Then the Hilbert space for the combined system of two particles is
\[\mathscr{H} = \mathscr{H}_A\otimes \mathscr{H}_B.\]
The symbol \(\otimes\) refers to a tensor product , a mathematical operation that combines two Hilbert spaces to form another Hilbert space. It is most easily understood in terms of explicit basis vectors: let \(\mathscr{H}_A\) be spanned by a basis \(\{|\mu_1\rangle, |\mu_2\rangle, |\mu_3\rangle, \dots\}\) , and \(\mathscr{H}_B\) be spanned by \(\{|\nu_1\rangle, |\nu_2\rangle, |\nu_3\rangle, \dots\}\) . Then \(\mathscr{H}_A \otimes \mathscr{H}_B\) is a space spanned by basis vectors consisting of pairwise combinations of basis vectors drawn from the \(\mathscr{H}_A\) and \(\mathscr{H}_B\) bases:
\[\Big\{\;\,|\mu_i\rangle\otimes|\nu_j\rangle \;\; \textrm{for} \; \textrm{all}\;\,|\mu_i\rangle,\; |\nu_j\rangle \;\,\Big\}.\]
Thus, if \(\mathscr{H}_A\) has dimension \(d_A\) and \(\mathscr{H}_B\) has dimension \(d_B\) , then \(\mathscr{H}_A\otimes \mathscr{H}_B\) has dimension \(d_A d_B\) . Any two-particle state can be written as a superposition of these basis vectors:
\[|\psi\rangle = \sum_{ij} \, c_{ij}\; |\mu_i\rangle \otimes |\nu_j\rangle.\]
The inner product between the tensor product basis states is defined as follows:
\[\Big(|\mu_i\rangle \otimes |\nu_j\rangle\;,\; |\mu_p\rangle \otimes |\nu_q\rangle \Big) \;\equiv\; \Big(\langle\mu_i| \otimes \langle\nu_j| \Big) \Big(|\mu_p\rangle \otimes |\nu_q\rangle\Big) \;\equiv\; \langle\mu_i|\mu_p\rangle \, \langle\nu_j|\nu_q\rangle = \delta_{ip}\delta_{jq}. \label{innerprod}\]
In other words, the inner product is performed “slot-by-slot”. We calculate the inner product for \(A\) , calculate the inner product for \(B\) , and then multiply the two resulting numbers. You can check that this satisfies all the formal requirements for an inner product in linear algebra (see Exercise 3.9.1).
For example, suppose \(\mathscr{H}_A\) and \(\mathscr{H}_B\) are both 2D Hilbert spaces describing spin- \(1/2\) degrees of freedom. Each space can be spanned by an orthonormal basis \(\{\,|\!+\!z\rangle, \,|\!-\!z\rangle \, \}\) , representing “spin-up” and “spin-down”. Then the tensor product space \(\mathscr{H}\) is a 4D space spanned by
\[\Big\{\;|\!+\!z\rangle\otimes|\!+\!z\rangle\,,\; |\!+\!z\rangle\otimes|\!-\!z\rangle\,,\; |\!-z\!\rangle\otimes|\!+\!z\rangle\,,\; |\!-\!z\rangle\otimes|\!-\!z\rangle \;\Big\}. \label{spin12}\]
We now make an important observation. If \(A\) is in state \(|\mu\rangle\) and \(B\) is in state \(|\nu\rangle\) , then the state of the combined system is fully specified: \(|\mu\rangle \otimes |\nu\rangle \in \mathscr{H}_A \otimes \mathscr{H}_B\) . But the reverse is not generally true! There exist states of the combined system that cannot be expressed in terms of definite states of the individual particles. For example, consider the following quantum state of two spin- \(1/2\) particles:
\[|\psi\rangle = \frac{1}{\sqrt{2}} \Big(|\!+\!z\rangle\otimes|\!-\!z\rangle \,-\, |\!-\!z\rangle\otimes|\!+\!z\rangle\Big). \label{entangled_state}\]
This state is constructed from two of the four basis states in \(\eqref{spin12}\), and you can check that the factor of \(1/\sqrt{2}\) ensures the normalization \(\langle\psi|\psi\rangle = 1\) with the inner product rule \(\eqref{innerprod}\). It is evident from looking at Equation \(\eqref{entangled_state}\) that neither \(A\) nor \(B\) possesses a definite \(|\!+\!z\rangle\) or \(|\!-\!z\rangle\) state. Moreover, we shall show (in Section 3.7) that there’s no choice of basis that allows this state to be expressed in terms of definite individual-particle states; i.e.,
\[|\psi\rangle \ne |\psi_A\rangle\otimes|\psi_B\rangle \;\;\;\textrm{for}\;\textrm{any}\;\; |\psi_A\rangle \in \mathscr{H}_A, \;|\psi_B\rangle \in \mathscr{H}_B.\]
In such a situation, the two particles are said to be entangled .
It is cumbersome to keep writing \(\otimes\) symbols, so we will henceforth omit the \(\otimes\) in cases where the tensor product is obvious. For instance,
\[\frac{1}{\sqrt{2}} \Big(|\!+\!z\rangle\otimes|\!-\!z\rangle \,-\, |\!-\!z\rangle\otimes|\!+\!z\rangle\Big) \;\;\equiv \;\; \frac{1}{\sqrt{2}} \Big(|\!+\!z\rangle|\!-\!z\rangle \,-\, |\!-\!z\rangle|\!+\!z\rangle\Big).\]
For systems of more than two particles, quantum states can be defined using multiple tensor products. Suppose a quantum system contains \(N\) particles described by the individual Hilbert spaces \(\{\mathscr{H}_1, \mathscr{H}_2, \dots, \mathscr{H}_N\}\) having dimensionality \(\{d_1, \dots, d_N\}\) . Then the overall system is described by the Hilbert space
\[\mathscr{H} = \mathscr{H}_1 \otimes \mathscr{H}_2 \otimes \cdots \otimes \mathscr{H}_N,\]
which has dimensionality \(d = d_1 d_2\cdots d_N\) . The dimensionality scales exponentially with the number of particles! For instance, if each particle has a 2D Hilbert space, a \(20\) -particle system has a Hilbert space with \(2^{20} =1\,048\,576\) dimensions. Thus, even in quantum systems with a modest number of particles, the quantum state can carry huge amounts of information. This is one of the motivations behind the active research field of quantum computing.
Finally, a proviso: although we refer to subsystems like \(A\) and \(B\) as “particles” for narrative convenience, they need not be actual particles. All this formalism applies to general subsystems—i.e., subsets of a large quantum system’s degrees of freedom. For instance, if a quantum system has a position eigenbasis for 3D space, the \(x\) , \(y\) , and \(z\) coordinates are distinct degrees of freedom, so each position eigenstate is really a tensor product:
\[|\,\mathbf{r} = (x,y,z)\,\rangle \;\equiv\; |x\rangle\, |y\rangle\, |z\rangle.\]
Also, if the subsystems really are particles, we are going to assume for now that the particles are distinguishable. There are other complications that arise if the particles are “identical”, which will be the subject of the next chapter (if you’re unsure what this means, just read on).


5.1: The Relationship between Physical Activity and Health
Find out how much you already know about physical activity by completing this ungraded quiz . Do you know more or less than you thought?
All Americans should be regularly physically active to improve overall health and fitness and to prevent many adverse health outcomes. The benefits of physical activity occur in generally healthy people, in people at risk of developing chronic diseases, and in people with current chronic conditions or disabilities. The Physical Activity Guidelines for Americans (2008) gives guidance on the amount of physical activity that will provide health benefits for all Americans. In addition to presenting the Guidelines, this Chapter gives an overview of research findings on physical activity and health.
Physical activity affects many health conditions, and the specific amounts and types of activity that benefit each condition vary. One consistent finding from research studies is that once the health benefits from physical activity begin to accrue, additional amounts of activity provide additional benefits.
Although some health benefits seem to begin with as little as 60 minutes (1 hour) a week, research shows that a total amount of 150 minutes (2 hours and 30 minutes) a week of moderate-intensity aerobic activity, such as brisk walking, consistently reduces the risk of many chronic diseases and other adverse health outcomes.
Watch the first three videos in this playlist about The Physical Activity Guidelines for Americans:
Examining the Relationship between Physical Activity and Health
In many studies covering a wide range of issues, researchers have focused on exercise , as well as on the more broadly defined concept of physical activity . Exercise is a form of physical activity that is planned, structured, repetitive, and performed with the goal of improving health or fitness. So, although all exercise is physical activity, not all physical activity is exercise.
Quick Review: What is the difference between physical activity and exercise?Studies have examined the role of physical activity in many groups—men and women, children, teens, adults, older adults, people with disabilities, and women during pregnancy and the postpartum period. These studies have focused on the role that physical activity plays in many health outcomes, including:
- Premature (early) death;
- Diseases such as coronary heart disease, stroke, some cancers, type 2 diabetes, osteoporosis, and depression;
- Risk factors for disease, such as high blood pressure and high blood cholesterol;
- Physical fitness, such as aerobic capacity , and muscle strength and endurance
- Functional capacity (the ability to engage in activities needed for daily living);
- Mental health, such as depression and cognitive function; and
- Injuries or sudden heart attacks.
These studies have also prompted questions as to what type and how much physical activity is needed for various health benefits. To answer this question, investigators have studied three main kinds of physical activity: aerobic, muscle-strengthening, and bone-strengthening.
Sources
Examining the Relationship between Physical Activity and Health: The Physical Activity Guidelines for Americans Office of Disease Prevention & Health Promotion, U.S. Department of Health and Human Services. http://www.health.gov/paguidelines/guidelines /


8.7: Works Consulted and Further Reading
Acemoglu, Daron, and James A. Robinson. 2013. Why Nations Fail: The Origins of Power, Prosperity, and Poverty. Reprint edition. New York, NY: Currency.
Flint, Colin, and Peter Taylor. 2011. Political Geography: World-Economy, Nation-State and Locality. 6 edition. London New York: Routledge.
Frost, Robert. “Mending Wall by Robert Frost.” Poetry Foundation. Accessed April 30, 2018. https://www.poetryfoundation.org/poe...6/mending-wall .
Gallaher, Carolyn, Carl T. Dahlman, Mary Gilmartin, Alison Mountz, and Peter Shirlow. 2009. Key Concepts in Political Geography. 1 edition. London ; Los Angeles: SAGE Publications Ltd.
Glassner, Martin Ira, and Chuck Fahrer. 2003. Political Geography. 3rd edition. Hoboken, NJ: John Wiley and Sons.
Jones, Martin, Rhys Jones, Michael Woods, Mark Whitehead, Deborah Dixon, and Matthew Hannah. 2015. An Introduction to Political Geography: Space, Place and Politics. 2 edition. London ; New York: Routledge.
Mann, Michael. 2012. The Sources of Social Power: Volume 1, A History of Power from the Beginning to AD 1760. 2 edition. New York: Cambridge University Press.
Marshall, Tim. 2015. Prisoners of Geography: Ten Maps That Explain Everything About the World. First Edition edition. New York, New York: Scribner.
Mungai, Christine. “Africa’s Borders Split over 177 Ethnic Groups, and Their ‘real’ Lines Aren’t Where You Think.” MG Africa. January 13, 2015. Accessed April 30, 2018. http://mgafrica.com/article/2015-01-...here-you-think .
Painter, Joe, and Alex Jeffrey. 2009. Political Geography. 2nd edition. Los Angeles: SAGE Publications Ltd.


8.9: Portfolio- Evidence and Objectivity
By the end of this section, you will be able to:
- Write about the development of your composing processes.
- Write about how composing processes affect your work.
- Write about your objectivity as a writer.
As you complete your report, think critically about your writing process. Watch An Introduction to Reflective Writing ( https://openstax.org/r/anintroductio...lectivewriting ) , and reflect on what you created from the first step of discovering ideas to the last steps of composing and editing the final draft.
Reflective Task: Lessons Learned
As you add your analytical report to your portfolio, write either a cover letter or a journal entry in which you respond to the following questions:
- How did you choose the topic for your report? Did you have to narrow or expand it?
- What methods did you use to gather ideas about your topic? What outside sources did you consult to gather information about your topic?
- How did you settle on your thesis? Did you rewrite it multiple times?
- What strategies did you use to organize your report?
- What strategies did you use to develop paragraphs? What difficulties, if any, did you encounter?
 Did you recognize your own biases? Was it difficult to write in third-person point of view?
- How did input from peers and other readers affect your drafting and revision processes? What specific constructive criticism did you receive that helped you?
- In what ways was this report easier or harder to write than other papers you have written?
- What could you have done differently to make writing your report easier or more effective?
Further Reading
The following books are just a few examples of in-depth book-length reporting.
Boo, Katherine. Behind the Beautiful Forevers: Life, Death, and Hope in a Mumbai Undercity . Random House, 2012.
Desmond, Matthew. Evicted: Poverty and Profit in the American City . Crown, 2016.
Ehrenreich, Barbara. Nickel and Dimed: On (Not) Getting By in America . Metropolitan Books, 2001.
Macy, Beth. Dopesick: Dealers, Doctors, and the Drug Company That Addicted America . Little, Brown, 2018.
Wilkerson, Isabel. The Warmth of Other Suns: The Epic Story of America’s Great Migration . Random House, 2010.
Works Cited
“About.” Barbara Ehrenreich , Hachette Book Group, www.barbaraehrenreich.com/.
Fowler, H. Ramsey, and Jane E. Aaron. The Little, Brown Handbook . 13th ed., Pearson, 2016.
McClure, Laura. “Fact-Checking 101.” TED-Ed Blog , TED-Ed, 30 Mar. 2017, blog.ed.ted.com/2017/03/30/ factchecking-101/.
“Professional, Technical Writing.” OWL: The Purdue Online Writing Lab , Purdue U, 2021, owl.purdue.edu/owl/ subject_specific_writing/professional_technical_writing/index.html.
“Reflective Writing in Education.” Research and Learning Online , Monash U, www.monash.edu/rlo/ assignment-samples/education/education-reflective-writing.


8.6.3: Tornadoes
Tornadoes
Tornadoes are the most powerful weather phenomenon known. A tornado is an intense system of low pressure with violent updrafts and converging winds. Though tornadoes have been intensely studied for years, the mechanism that actually creates them still eludes us. Tornadoes have been documented in most all the regions of the Earth, though they are most prevalent in the United States.
Tornadoes are spawned from severe thunderstorms. Wind shear, where winds are traveling at different speeds and from different directions aloft cause rotation of air about a horizontal axis within the thunderstorm. The rotating circulation is tilted into the vertical by the updrafts of air in a severe thunderstorm. As the rotating air increases in height and shrinks in size a mesocyclone is formed. For whatever reason, a tornado funnel is spawned within the mesocyclone.
The funnel can remain aloft, twisting and turning without wreaking much havoc below, but is most destructive when it touches the ground. A tornado can vary in diameter from a few hundred feet to greater than a mile. Tornadoes typically move across the surface at speeds ranging from 22 - 33 mph (10 - 15 meters per second). [ Watch "Hunt for the Supertwister from PBS].
Tornadoes that develop over water are called waterspouts . Waterspouts my orignate over water or a tornado passes from land to water. View the video "Watersputs" for more.
Video : "Waterspouts". (Courtesy of NOAA)
The central U.S. contains a unique mix of topography and weather factors that combine to create these ferocious weather systems. The most favorable situation for these storms to develop is during the months of April through June when there is the most contrast between air masses in the central United States. The region of highest concentration is that of "tornado alley", a region that stretches from eastern Nebraska through central Kansas and Oklahoma in to the panhandle of Texas. The tornado season varies with latitude, with the southeastern U.S. season from January through March and the north central states during July through September. On April 3, 1974 148 tornadoes struck 13 states leaving a swath of death and destruction across the U.S.
Tornadoes are categorized on the basis of their destruction by the Enhanced Fujita scale. The scale assigns a tornado a 'rating' based on estimated wind speeds and related damage. Several damage indicators, e.g., trees, motels, strip malls are used to estimate wind speeds and classify the tornado. In the May 24, 2013 NPR Talk of the Nation segment " Tracking Killer Tornadoes " , Marshall Shepherd, the president of the American Meteorological Society, describes the ingredients of major tornadoes, and how they are predicted.
 (Courtesy of National Geographic)
Learn more about the destructive effect of tornadoes by "Digging Deeper: The April 27, 2011 Southern USA Tornado Outbreak".
April 27-28, 2011 the southeastern United States was struck by an estimated 211 tornadoes. Wreaking havoc over eight states, more than 340 people lost their lives as whole towns were destroyed across Alabama, Arkansas, Georgia, Mississippi, North Carolina, Tennessee, and Virginia. It was the most deadly day since March 18, 1925 when 747 people died.
Video: GOES satellite image animation. (Courtesy NASA Earth Observatory)
The perfect conditions for tornado development were closely monitored by the National Weather Service days prior to the events of April 27-28. Warm, moist air at the surface streamed ashore from the Gulf of Mexico. With cold air aloft, highly unstable atmospheric conditions ahead of a strong cold front sweeping drier air behind it. A strong westerly jet stream aloft combined with surface winds from the south and east triggered strong vertical wind shear providing lift to the air. Using composite indices based on these conditions, NOAA's Storm Prediction center issued a "high risk" alert for tornadic conditions more than 12 hours in advance. Beginning in the afternoon of the 26 th , thunderstorms exploded in the unstable air. The National Weather Service's worst nightmare was about to come true.
Video: April 27, 2011 Tornado Outbreak (Courtesy NOAA Weather Partners Video Library)Across the southern United States roared a storm system producing some of the largest tornadoes on earth, supertwisters . A rare EF-5 tornado a half mile wide ripped through the community of Smithville, Mississippi at 3:44 pm on the April 27. With estimated peak winds of 205 mph, dozens of homes and businesses were pulled from their foundations. The town's water system was destroyed. Most trees were broken, twisted and stripped of their bark. A second F5 tornado touched down near Hackleburg, Alabama. It was the first time since 1990 that two F5 supertwisters formed on the same day.
Barely a month later, Joplin Missouri was struck by a multi-vortex EF5 tornado on May 22, 201. Estimated at 1.21 km (.75 miles) wide, as it tracked at least 11 km (7 miles) across the city. With winds over 200 mph. Over 125 people were killed and hundreds injured making it the deadliest since modern records have been kept and the eighth-deadliest single tornado in U.S. history.


9.2: Work Group Structure
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2. How do group norms, roles, and status systems affect employee behavior and performance?
Work group structure can be characterized in many different ways. We examine several characteristics that are useful in describing and understanding what makes one group different from another. This matrix of variables will, when taken together, paint a portrait of work groups in terms of relatively enduring group properties. The aspects of group structure to be considered are (1) work roles, (2) work group size, (3) work group norms, (4) status relationships, and (5) work group cohesiveness. Each of these factors has been shown to influence group processes, as shown in Exhibit 9.3 . Thus, the material presented here will be important when we focus on group processes later in the text.
Work Roles
In order to accomplish its goals and maintain its norms, a group must differentiate the work activities of its members. One or more members assume leadership positions, others carry out the major work of the group, and still others serve in support roles. This specialization of activities is commonly referred to as role differentiation. More specifically, a work role is an expected behavior pattern assigned or attributed to a particular position in the organization. It defines individual responsibilities on behalf of the group.
It has been suggested that within organizational settings, work roles can be divided into three types on the basis of the nature of the activities that encompass the role. 6 These are:
- Task-oriented roles. These roles focus on task-related activities aimed at achieving group performance goals.
- Relations-oriented roles. These roles emphasize the further development of the group, including building group cohesiveness and consensus, preserving group harmony, looking after group member welfare, and so forth.
- Self-oriented roles. These roles emphasize the specific needs and goals of individual members, often at the expense of the group.
As we might expect, individual group members often perform several of these roles simultaneously. A group leader, for example, must focus group attention on task performance while at the same time preserving group harmony and cohesiveness. To see how this works, consider your own experience. You may be able to recognize the roles you have played in groups you have been a member of. In your experience, have you played multiple roles or single roles?
Perhaps the best way to understand the nature of work roles is to examine a role episode . A role episode is an attempt to explain how a particular role is learned and acted upon. As can be seen in Exhibit 9.4 , a role episode begins with members’ expectations about what one person should be doing in a particular position (Stage 1). These expectations are then communicated to the individual (Stage 2), causing the individual to perceive the expectations about the expected role (Stage 3). Finally, the individual decides to act upon the role in terms of actual role-related behavior (Stage 4). In other words, Stages 1 and 2 deal with the expected role, whereas Stage 3 focuses on the perceived role and Stage 4 focuses on the enacted role.
Consider the following simple example. A group may determine that its newest member is responsible for getting coffee for group members during breaks (Stage 1). This role is then explained to the incoming member (Stage 2), who becomes aware of his or her expected role (Stage 3). On the basis of these perceptions (and probably reinforced by group norms), the individual then would probably carry out the assigned behavior (Stage 4).
Several aspects of this model of a role episode should be noted. First, Stages 1 and 2 are initiated by the group and directed at the individual. Stages 3 and 4, on the other hand, represent thoughts and actions of the individual receiving the stimuli. In addition, Stages 1 and 3 represent cognitive and perceptual evaluations, whereas Stages 2 and 4 represent actual behaviors. The sum total of all the roles assigned to one individual is called the role set .
Although the role episode presented here seems straightforward, in reality we know that it is far more complicated. For instance, individuals typically receive multiple and sometimes conflicting messages from various groups, all attempting to assign them a particular role. This can easily lead to role conflict . Messages sent to an individual may sometimes be unclear, leading to role ambiguity . Finally, individuals may simply receive too many role-related messages, contributing to role overload . Discussion of these topics is reserved for later study, where examination of several important aspects of psychological adjustment to work.
Work Group Size
Obviously, work groups can be found in various sizes. Early management theorists spent considerable time and effort to no avail attempting to identify the right size for the various types of work groups. There is simply no right number of people for most group activities. They did, however, discover a great deal about what happens as group size increases. 7 A number of relevant size outcome relationships are summarized in Table 9.2 .
Group Interaction Patterns. First, we will consider the effects of variations in group size on group interaction patterns. A series of classic studies by Bales and Borgatta examined this issue using a technique known as interaction process analysis . 8 This technique records who says what to whom; through using it, Bales and his colleagues found that smaller groups (2–4 persons) typically exhibited greater tension, agreement, and opinion seeking, whereas larger groups (13–16 persons) showed more tension release and giving of suggestions and information. This suggests that harmony is crucial in smaller groups and that people in them have more time to develop their thoughts and opinions. On the other hand, individuals in larger groups must be more direct because of the increased competition for attention.
Job Attitudes. Increases in workgroup size are fairly consistently found to be inversely related to satisfaction, although the relationship is not overly strong. 9 That is, people working in smaller work units or departments report higher levels of satisfaction than those in larger units. This finding is not surprising in view of the greater attention one receives in smaller groups and the greater importance group members typically experience in such things as their role set.
Absenteeism and Turnover. Available research indicates that increases in work group size and absenteeism are moderately related among blue-collar workers, although no such relationship exists for white-collar workers. 10 One explanation for these findings is that increased work group size leads to lower group cohesiveness, higher task specialization, and poorer communication. As a result, it becomes more difficult to satisfy higher-order needs on the job, and job attendance becomes less appealing. This explanation may be more relevant in the case of blue-collar workers, who typically have little job autonomy and control. White-collar workers typically have more avenues available to them for need satisfaction. Similar findings exist for employee turnover. Turnover rates are higher in larger groups. 11 It again can be hypothesized that because larger groups make need satisfaction more difficult, there is less reason for individuals to remain with the organization.
Productivity. No clear relationship has been found between group size and productivity. 12 There is probably a good reason for this. Unless we take into consideration the type of task that is being performed, we really cannot expect a clear or direct relationship. Mitchell explains it as follows:
Think of a task where each new member adds a new independent amount of productivity (certain piece-rate jobs might fit here). If we add more people, we will add more productivity. . . . On the other hand, there are tasks where everyone works together and pools their resources. With each new person the added increment of new skills or knowledge decreases. After a while increases in size will fail to add much to the group except coordination and motivation problems. Large groups will perform less well than small groups. The relationship between group size and productivity will therefore depend on the type of task that needs to be done. 13
However, when we look at productivity and group size, it is important to recognize the existence of a unique factor called social loafing , 14 a tendency for individual group members to reduce their effort on a group task. This phenomenon occurs when (1) people see their task as being unimportant or simple, (2) group members think their individual output is not identifiable, and (3) group members expect their fellow workers to loaf. Social loafing is more prevalent in larger groups than in smaller groups, presumably because the above three factors are accentuated. From a managerial standpoint, this problem can be reduced by providing workers with greater responsibility for task accomplishment and more challenging assignments. This issue is addressed in the following chapter on job design.
Work Group Norms
The concept of work group norms represents a complex topic with a history of social psychological research dating back several decades. In this section, we will highlight several of the essential aspects of norms and how they relate to people at work. We will consider the characteristics and functions of work group norms as well as conformity with and deviance from them.
Characteristics of Work Group Norms. A work group norm may be defined as a standard that is shared by group members and regulates member behavior within an organization. An example can be seen in a typical classroom situation when students develop a norm against speaking up in class too often. It is believed that students who are highly visible improve their grades at the expense of others. Hence, a norm is created that attempts to govern acceptable classroom behavior. We see similar examples in the workplace. There may be a norm against producing too much or too little, against getting too close to the supervisor, against being late for work, and so forth.
Work group norms may be characterized by at least five factors: 15
- Norms summarize and simplify group influence processes. They denote the processes by which groups regulate and regularize member behavior.
- Norms apply only to behavior, not to private thoughts and feelings. Although norms may be based on thoughts and feelings, they cannot govern them. That is, private acceptance of group norms is unnecessary—only public compliance is needed.
- Norms are generally developed only for behaviors that are viewed as important by most group members.
- Norms usually develop gradually, but the process can be quickened if members wish. Norms usually are developed by group members as the need arises, such as when a situation occurs that requires new ground rules for members in order to protect group integrity.
- All norms do not apply to all members. Some norms, for example, apply only to young initiates (such as getting the coffee), whereas others are based on seniority, sex, race, or economic class.
Functions of Work Group Norms. Most all groups have norms, although some may be more extensive than others. To see this, examine the norms that exist in the various groups to which you belong. Which groups have more fully developed norms? Why? What functions do these norms serve? Several efforts have been made to answer this question. In general, work group norms serve four functions in organizational settings: 16
- Norms facilitate group survival . When a group is under threat, norms provide a basis for ensuring goal- directed behavior and rejecting deviant behavior that is not purposeful to the group. This is essentially a “circle the wagons” phenomenon.
- Norms simplify expected behaviors . Norms tell group members what is expected of them—what is acceptable and unacceptable—and allow members to anticipate the behaviors of their fellow group members and to anticipate the positive or negative consequences of their own behavior.
- Norms help avoid embarrassing situations . By identifying acceptable and unacceptable behaviors, norms tell group members when a behavior or topic is damaging to another member. For example, a norm against swearing signals group members that such action would be hurtful to someone in the group and should be avoided.
- Norms help identify the group and express its central values to others . Norms concerning clothes, language, mannerisms, and so forth help tell others who belongs to the group and, in some cases, what the group stands for. Norms often serve as rallying points for group members.
Conformity and Deviance. Managers often wonder why employees comply with the norms and dictates of their work group even when they seemingly work against their best interests. This concern is particularly strong when workers intentionally withhold productivity that could lead to higher incomes. The answer to this question lies in the concept of conformity to group norms. Situations arise when the individual is swept along by the group and acts in ways that he would prefer not to.
To see how this works, consider the results of a classic study of individual conformity to group pressures that was carried out by Solomon Asch. 17 Asch conducted a laboratory experiment in which a native subject was placed in a room with several confederates. Each person in the room was asked to match the length of a given line ( X ) with that of one of three unequal lines ( A, B, and C ). This is shown in Exhibit 9.5 . Confederates, who spoke first, were all instructed prior to the experiment to identify line C as the line most like X, even though A was clearly the answer. The results were startling. In over one-third of the trials in the experiment, the naive subject denied the evidence of his own senses and agreed with the answers given by the unknown confederates. In other words, when confronted by a unanimous answer from others in the group, a large percentage of individuals chose to go along with the group rather than express a conflicting opinion, even though these individuals were confident their own answers were correct.
What causes such conformity to group norms? And, under what conditions will an individual deviate from these norms? Conformity to group norms is believed to be caused by at least three factors. 18 First, personality plays a major role. For instance, negative correlations have been found between conformity and intelligence, tolerance, and ego strength, whereas authoritarianism was found to be positively related. Essentially, people who have a strong self-identity are more likely to stick to their own norms and deviate from those of the group when a conflict between the two exists. Second, the initial stimulus that evokes responses can influence conformity. The more ambiguous the stimulus (e.g., a new and confusing order from top management), the greater the propensity to conform to group norms (“I’m not sure what the new order from management really means, so I’ll just go along with what others think it means”). In this sense, conformity provides a sense of protection and security in a new and perhaps threatening situation. Finally, group characteristics themselves can influence conformity to group norms. Factors such as the extent of pressure exerted on group members to conform, the extent to which a member identifies with the group, and the extent to which the group has been successful in achieving previous goals can influence conformity.
What happens when someone deviates from group norms? Research indicates that groups often respond by increasing the amount of communication directed toward the deviant member. 19 This communication is aimed at bringing the deviant into the acceptable bounds set by the group. A good example of this process can be seen in Janis’s classic study of the group processes leading up to the abortive Bay of Pigs invasion in Cuba. 20 At one meeting, Arthur Schlesinger, an adviser to President Kennedy, expressed opposition to the plan even though no one else expressed similar doubts. After listening to his opposition for a while, Robert Kennedy took Schlesinger aside and said, “You may be right or you may be wrong, but the President has his mind made up. Don’t push it any further. Now is the time for everyone to help him all they can.” Janis elaborated on this group decision-making process and termed it “groupthink.”
When a deviant member refuses to heed the message and persists in breaking group norms, group members often respond by rejecting or isolating the deviant. They tell the deviant, in essence, that they will no longer tolerate such behavior and prefer to reconstitute the group. If the deviant is not expelled, the group must continually confront behavior that conflicts with what it holds to be true. Rather than question or reexamine its beliefs, the group finds it simpler—and safer—to rid itself of dangerous influences.
Status Systems
A fourth characteristic, or structural property, of work groups is the status system. Status systems serve to differentiate individuals on the basis of some criterion or set of criteria. There are five general bases on which status differentiations are made: birth, personal characteristics, achievement, possessions, and formal authority. All five bases can be seen as establishing status in work groups. For example, an employee may achieve high status because he is the boss’s son (birth), the brightest or strongest member of the group (personal characteristics), the best performer (achievement), the richest or highest paid (possessions), or the foreman or supervisor (formal authority).
Reasons for Status Systems. Status systems can be seen throughout most organizations. We differentiate between blue-collar and white-collar employees (and even pink and gold collar), skilled tradespersons and unskilled workers, senior and junior managers, high achievers and low achievers, and popular and unpopular employees. Why do we do this? In essence, status differentiation in organizations (and their related status symbols) serves four purposes: 21
Motivation. We ascribe status to persons as rewards or incentives for performance and achievement. If high achievement is recognized as positive behavior by an organization, individuals are more willing to exert effort.
Identification. Status and status symbols provide useful cues to acceptable behavior in new situations. In the military, for example, badges of rank quickly tell members who has authority and who is to be obeyed. Similarly, in business, titles serve the same purpose.
Dignification. People are often ascribed status as a means of signifying respect that is due them. A clergyman’s attire, for instance, identifies a representative of the church.
Stabilization. Finally, status systems and symbols facilitate stabilization in an otherwise turbulent environment by providing a force for continuity. Authority patterns, role relationships, and interpersonal interactions are all affected and, indeed, defined by the status system in effect. As a result, much ambiguity in the work situation is reduced.
Status can be conferred on an individual in many different ways. One way common in organizations is through the assignment and decoration of offices. John Dean, counsel to former President Nixon, provides the following account concerning status in the White House:
Everyone [on the White House Staff] jockeyed for a position close to the President’s ear, and even an unseasoned observer could sense minute changes in status. Success and failure could be seen in the size, decor, and location of offices. Anyone who moved into a smaller office was on the way down. If a carpenter, cabinetmaker, or wallpaper hanger was busy in someone’s office, this was the sure sign he was on the rise. Every day, workmen crawled over the White House complex like ants. Movers busied themselves with the continuous shuffling of furniture from one office to another as people moved in, up, down, or out. We learned to read office changes as an index of the internal bureaucratic power struggles. The expense was irrelevant to Haldeman. . . . He once retorted when we discussed whether we should reveal such expense, “This place is a national monument, and I can’t help it if the last three Presidents let it go to hell.” Actually, the costs had less to do with the fitness of the White House than with the need of its occupants to see tangible evidence of their prestige. 22
Modern businesses looking to attract top talent do not have office spaces that have a group of workers siloed in their own walled-off offices with doors 20 years old. 23
One Orlando business, for instance, spent about $330,000 on the design and build-out of its space.
Status Incongruence. An interesting aspect of status systems in organizations is the notion of status incongruence . This situation exists when a person is high on certain valued dimensions but low on others, or when a person’s characteristics seem inappropriate for a particular job. Examples of status incongruence include the college student who takes a janitorial job during the summer (usually referred to as the “college kid” by the other janitors), the president’s son who works his way up through the organizational hierarchy (at an accelerated rate, needless to say), or the young fast-track manager who is promoted to a level typically held by older employees.
Status incongruence presents problems for everyone involved. The individual may become the target of hostility and jealousy from coworkers who feel the individual has risen above his station. The coworkers, on the other hand, may be forced to acknowledge their own lack of success or achievement. One might ask, for example, “Why has this youngster been promoted over me when I have more seniority?” At least two remedies for this conflict are available to managers. An organization can (1) select or promote only those individuals whose characteristics are congruent with the job and work group, and (2) attempt to change the values of the group. Neither of these possibilities seems realistic or fair. Hence, dynamic organizations that truly reward high achievement (instead of seniority) must accept some level of conflict resulting from status incongruence.
expanding around the globe
Status Systems in Japanese Business
In Japan, etiquette is not simply a prescription for appropriate social responses, it is a complete guide to conducting oneself in all social interactions. At the root of this system of social interaction is one’s status within the organization and society.
The effects of status in Japan can be seen in many ways. For example, when two businesspeople meet for the first time, they exchange business cards—before they even say hello to each other. After carefully reading the cards, each knows precisely the other’s rank (and status) in the organizational hierarchy and, thus, how to respond. The person with the lower status must bow lower than the person with the higher status.
Moreover, when four managers get into a car, status determines where each will sit. This is shown in Exhibit 9.6 , where it can be seen that the most important (highest-status) manager will sit in the back seat, directly behind the driver. Similarly, when four managers enter an elevator, the least senior stands in front of the elevator controls, with the most senior behind. In a meeting room or in a restaurant, the most honored seat is farthest from the door, whereas the least honored is nearest the door. Even within the meeting room itself, a sofa is considered higher in rank than armchairs.
Clearly, status plays an important role in Japanese (and several other East Asian) societies. Status recognizes age (an important cultural variable in these societies) and tells everyone involved how to behave. Though such prescriptive practices may seem strange to many Westerners, it is quite natural in Japan. In fact, many Japanese feel such guidelines are helpful and convenient in defining social relationships, avoiding awkward situations, and making business transactions more comfortable and productive. Whether or not this perception is accurate, status systems are a fact of life that must be recognized by Western managers attempting to do business in Asia. Failure to understand such social patterns puts the Western manager at a distinct disadvantage.
Sources: Allison, “Useful Japanese Business Manners to Impress a Client or Guest,” Fast Japan , October 21, 2016; M. Yazinuma and R. Kennedy, “Life Is So Simple When You Know Your Place,” Intersect, May 1986, pp. 35–39.
Group Cohesiveness
A fifth characteristic of work groups is group cohesiveness. We have all come in contact with groups whose members feel a high degree of camaraderie, group spirit, and unity. In these groups, individuals seem to be concerned about the welfare of other group members as well as that of the group as a whole. There is a feeling of “us against them” that creates a closeness among them. This phenomenon is called group cohesiveness. More specifically, group cohesiveness may be defined as the extent to which individual members of a group are motivated to remain in the group. According to Shaw, “Members of highly cohesive groups are more energetic in group activities, they are less likely to be absent from group meetings, they are happy when the group succeeds and sad when it fails, etc., whereas members of less cohesive groups are less concerned about the group’s activities.” 24
We shall consider two primary aspects of work group cohesiveness. First, we look at major causes of cohesiveness. Following this, we examine its consequences. Determinants of Group Cohesiveness. Why do some work groups develop a high degree of group cohesiveness while others do not? To answer this question, we have to examine both the composition of the group and several situational variables that play a role in determining the extent of cohesiveness. The major factors that influence group cohesiveness are shown in Exhibit 9.7 . 25 These include the following:
- Group homogeneity . The more homogeneous the group—that is, the more members share similar characteristics and backgrounds—the greater the cohesiveness.
- Group maturity . Groups tend to become more cohesive simply as a result of the passage of time. Continued interaction over long periods of time helps members develop a closeness born of shared experiences.
- Group size . Smaller groups have an easier time developing cohesiveness, possibly because of the less complex interpersonal interaction patterns.
- Frequency of interaction . Groups that have greater opportunities to interact on a regular or frequent basis tend to become more cohesive than groups that meet less frequently or whose members are more isolated.
- Clear group goals . Groups that know exactly what they are trying to accomplish develop greater cohesiveness, in part because of a shared sense of mission and the absence of conflict over mission.
- Competition or external threat . When groups sense external threat or hostility, they tend to band together more closely. There is, indeed, “safety in numbers.”
- Success . Group success on a previous task often facilitates increased cohesiveness and a sense of “we did it together.”
In other words, a wide variety of factors can influence work group cohesiveness. The precise manner in which these processes occur is not known. Even so, managers must recognize the existence of certain forces of group cohesiveness if they are to understand the nature of group dynamics in organizations. The second aspect of group cohesiveness that must be understood by managers relates to their consequences.
Consequences of Group Cohesiveness. As shown in Exhibit 9.7 , several consequences of group cohesiveness can also be identified. The first and most obvious consequence is maintenance of membership . If the attractiveness of the group is sufficiently stronger than the attractiveness of alternative groups, then we would expect the individual to remain in the group. Hence, turnover rates should be low.
In addition, high group cohesiveness typically provides the group with considerable power over group members . The power of a group over members depends upon the level of outcomes members expect to receive from the group compared to what they could receive through alternate means. When the group is seen as being highly instrumental to achieving personal goals, individuals will typically submit to the will of the group.
Third, members of highly cohesive groups tend to exhibit greater participation and loyalty . Several studies have shown that as cohesiveness increases, there is more frequent communication among members, a greater degree of participation in group activities, and less absenteeism. Moreover, members of highly cohesive groups tend to be more cooperative and friendly and generally behave in ways designed to promote integration among members.
Fourth, members of highly cohesive groups generally report high levels of satisfaction . In fact, the concept of group cohesiveness almost demands all this be the case, because it is unlikely that members will feel like remaining with a group with which they are dissatisfied.
Finally, what is the effect of group cohesiveness on productivity ? No clear relationship exists here. Instead, research shows that the extent to which cohesiveness and productivity are related is moderated by the extent to which group members accept organizational goals. This is shown in Exhibit 9.8 . Specifically, when cohesiveness and acceptance of organizational goals are high, performance will probably be high. When acceptance is high but cohesiveness is low, group performance will typically be moderate. Finally, performance will generally be low when goal acceptance is low regardless of the extent of group cohesiveness. In other words, high performance is most likely to result when highly cohesive teams accept the goals of the organization. At this time, both forces for performance are congruent.
managing change
Group Cohesiveness
In the fast-moving innovative car industry, it is always important to be thinking about improving and staying ahead of the competition. For Ford and Chevrolet however, they have such popular vehicles—the F-150 and the hybrid Volt, respectively—that finding ways to improve them without taking away the qualities that make them popular is key.
With the F-150, Ford had one of the best-selling vehicles for more than 30 years, but improving upon their most popular vehicle came with its challenges. In 2015, the team wanted to introduce an economically six-cylinder EcoBoost engine, and an all-aluminum body. The team was worried about the marketplace and hoped that the customers would accept the change to their beloved truck.
The planning started 18 months before, working in parallel work teams on various parts of the project. Each team was responsible for a piece of the overall project, and they frequently came together to make sure that they were working cohesively to create a viable vehicle. The most successful piece of the dynamic for Ford was teams’ ability to share feedback. Pete Reyes expresses the teamwork mentality: “Everybody crosses boundaries, and they came back with all of the feedback that shaped what we are going to do.”
Having team cohesiveness was ultimately what brought Ford to the finish line. With over 1,000 members of the overall team, employees were able to accomplish a truly viable vehicle that weighed 700 pounds less, as well as countless other innovations that gave the truck 29 percent more fuel economy.
“We stuck to common goals . . . I don’t think I’ll ever work on a team that tight again,” stated Reyes about his team of developmental managers. As a result of their close teamwork, Ford announced third- quarter earnings of 1.9 billion, an increase of 1.1 billion from 2014.
Questions:
- What challenges does a large project like Ford’s F-150 project have to take into account for success?
- What kind of work teams did Ford employ throughout its project to get the best results?
- Can Ford’s successes be translated into other smaller teams? How would you apply its best practices to a work environment of your own?
Sources: J. Motivalli, “ 5 Inspiring Companies That Rely on Teamwork to Be Successful,” Success , February 16, 2016, https://www.success.com/5-inspiring-...be-successful/ ; “All-New 2015 F-150 Most Patented Truck in Ford History – New Innovations Bolster Next-Generation Light- Duty Pickup,” Ford Media Center , May 23, 2014, media.ford.com/content/fordmedia/fna/us/en/ news/2014/05/23/all-new-2015-f-150-most-patented-truck-in-ford-history--new-inno.html; P. Friedman, “Body of Work,” Ford Corporate Website, accessed, December 13, 2018, corporate.ford.com/ innovation/f-150-body-of-work.html.
concept check
- Explain what work roles are.
- What role does group size play in the interactions of group members?
- What are group norms and what role do they play toward group cohesiveness?


2: Chemical Equilibrium
In this chapter, you will learn how to predict the position of the balance and the yield of a product of a reaction under specific conditions, how to change a reaction's conditions to increase or reduce yield, and how to evaluate an equilibrium system's reaction to disturbances.
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- 2.0: Prelude to Equilibrium
- Reactions can occur in both directions simultaneously (reactants to products and products to reactants) and eventually reach a state of balance. Reactions can occur in both directions simultaneously (reactants to products and products to reactants) and eventually reach a state of balance.
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- 2.1: Chemical Equilibria
- A reaction is at equilibrium when the amounts of reactants or products no longer change. Chemical equilibrium is a dynamic process, meaning the rate of formation of products by the forward reaction is equal to the rate at which the products re-form reactants by the reverse reaction.
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- 2.2: Free Energy and the Equilibrium Constant
- For a reversible process (with no external work), the change in free energy can be expressed in terms of volume, pressure, entropy, and temperature. If the products and reactants are in their standard states and ΔG° < 0, then K > 1, and products are favored over reactants at equilibrium. If ΔG° > 0, then K < 1, and reactants are favored over products at equilibrium. If ΔG° = 0, then K=1, and neither reactants nor products are favored at equilibrium. We can use the measured equilibrium constant
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- 2.3: Equilibrium Constants
- For any reaction that is at equilibrium, the reaction quotient Q is equal to the equilibrium constant K for the reaction. If a reactant or product is a pure solid, a pure liquid, or the solvent in a dilute solution, the concentration of this component does not appear in the expression for the equilibrium constant. At equilibrium, the values of the concentrations of the reactants and products are constant and the reaction quotient will always equal K.
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- 2.4: Shifting Equilibria - Le Châtelier’s Principle
- Systems at equilibrium can be disturbed by changes to temperature, concentration, and, in some cases, volume and pressure; volume and pressure changes will disturb equilibrium if the number of moles of gas is different on the reactant and product sides of the reaction. The system's response to these disturbances is described by Le Châtelier's principle: The system will respond in a way that counteracts the disturbance. Not all changes to the system result in a disturbance of the equilibrium.
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- 2.5: Equilibrium Calculations
- The ratios of the rate of change in concentrations of a reaction are equal to the ratios of the coefficients in the balanced chemical equation. The sign of the coefficient of X is positive when the concentration increases and negative when it decreases. We learned to approach three basic types of equilibrium problems. When given the concentrations of the reactants and products at equilibrium, we can solve for the equilibrium constant.
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- 2.E: Fundamental Equilibrium Concepts (Exercises)
- These are homework exercises to accompany the Textmap created for "Chemistry" by OpenStax. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.
Contributors
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


1.72: Modulated crystal structure
A modulated crystal structure is a density (or atom arrangement) that may be obtained from a density (or atom arrangement) with space-group symmetry by a finite density change (or finite displacement of each atom, respectively) that is (quasi)periodic. A function or a displacement field is periodic if it is invariant under a lattice of translations. Then its Fourier transform consists of δ-peaks on a reciprocal lattice that spans the space and is nowhere dense. A quasiperiodic function has a Fourier transform consisting of δ-peaks on a vector module of finite rank. This means that the peaks may be indexed with integers using a finite number of basis vectors . If the modulation consists of deviations from the basic structure in the positions, the modulation is displacive ( displacive modulation ) . When the probability distribution deviates from that in the basic structure the modulation is occupational.
See also
Model for a displacively modulated crystal structure . The basic structure is two-dimensional rectangular, with lattice constants a and b , the modulation wave vector is in the b -direction, the wavelength of the periodic modulation is λ such that λ/ b is an irrational number.


1.8: Activated Sludge
Learning Outcomes
- Compare and contrast the difference between fixed film and suspended growth biological treatment systems
- Describe how the activated sludge process can more efficiently reduce organic wastes
- Understand how different process control strategies work in an activated sludge system
- Examine how a secondary clarifier is utilized in an activated sludge system
Suspended Growth Processes
Unlike the fixed film biological systems discussed in Chapter 7, activated sludge uses a suspended growth process. This means that there is no media for the bacteria to become fixed to. The microorganisms are suspended in the tanks either by a mixer or air diffusers and are then mixed in with the incoming wastewater. This mixture of wastewater and microorganisms is referred to as the Mixed Liquor Suspended Solids (MLSS). A sample can be taken from the activated sludge system and analyzed in a laboratory to determine how many mg/L there are of MLSS in the system. This laboratory result will be a critical design and operational parameter that will need to be continually monitored to ensure effective treatment.
Activated Sludge Treatment
The activated sludge process was developed by two scientists, Edward Arden and William Lockett, in England in 1914. Their experiments showed that by taking the microorganisms that were already established from aerobic decomposition and introducing them to fresh wastewater, it would speed up the decomposition of the new organic wastes. Instead of relying on the 30 to 45 days that it would normally take to breakdown these organic wastes, the activated sludge process can achieve the same level of treatment in less than one day. This means that an activated sludge wastewater treatment system will be able to handle higher flow rates and higher organic loading than pond treatment or fixed film systems.
To achieve this on a large scale, conventional activated sludge systems are comprised of an aeration tank followed by a secondary clarifier. In the secondary clarifier, the microorganisms will separate from the now treated wastewater. A majority of those microorganisms will be returned back to the reactor and are now activated to treat more of the incoming wastewater. In the aeration tanks, the bacteria are in an environment with dissolved oxygen readily available and organic matter to consume. Like the other biological processes, this is how the reduction of BOD5 occurs, through aerobic decomposition. What makes activated sludge unique is that in the secondary clarifier, the bacteria become stressed because their food source has been drastically decreased and there is no more dissolved oxygen. They begin to go through endogenous respiration. The bacteria basically become so starved that they begin to breakdown their own cellular structure. Before the bacteria completely cannibalize themselves, they are sent back to the aeration tank where they are re-introduced to readily available dissolved oxygen and organic matter. The starved bacteria are then able to rapidly re-start aerobic decomposition and quickly reduce the BOD5 in the wastewater.
Food to Microorganism Ratio
A key parameter to determine the effectiveness of activated sludge systems is the food to microorganism ratio, or F/M. The food is determined by the amount of BOD5 in the incoming wastewater and the amount of microorganisms available to consume that food is determined by the amount of MLSS in the aeration tanks. Since it’s a ratio, the units of these two laboratory results must be the same. The mg/L concentration of the laboratory results is converted into a mass with the units of lbs. While each treatment plant will determine which level of F/M has historically given effective treatment, a common range is around 0.2 to 0.5.
Return Activated Sludge
The return activated sludge, or RAS, are the bacteria that have settled in the secondary clarifier and are being sent back to the aeration tank. The rate of speed at which the microorganisms are returned is something that the operator can control.
Waste Activated Sludge (WAS)
Like the other biological process discussed, the bacteria, overtime will grow and their population will increase. To control the amount of bacteria in the system, a portion of the RAS will not be returned to the aeration tank but instead is directed to a separate solids handling treatment unit. Typically, these solids are combined with the settled solids from the primary sedimentation tanks and sent to an anaerobic digester. After anaerobic digestions, the solids will be dewatered and ultimately sent to a landfill for disposal.
How much bacteria remains in the system and how much is wasted can be determined by the mean cell residence time or MCRT. The MCRT is a theoretical calculation of the average time a single bacteria will stay within the activated sludge system before being wasted. To calculate the MCRT an operator would determine how many pounds of MLSS there is in the system and divide that by how many pounds were removed from the system.
Process Control
The F/M ratio, MCRT, RAS, WAS, and dissolved oxygen concentrations can all be manipulated by the operators of a wastewater treatment facility to optimize the effectiveness of treatment. In fact, those parameters are the only things that can be easily controlled. The amount of incoming wastewater is going to be what it is and it will fluctuate throughout a 24 hour period as well as vary by season. The incoming BOD5 loading is what it’s going to be and the operators can’t control it.
If the F/M is too low, it means that there are more bacteria than what is needed to consume the available food. This is inefficient because supplying oxygen to the bacteria requires a significant amount of energy. If there is too much bacteria in the system and not enough food, the bacteria will still be consuming oxygen but the BOD5 won’t be further reduced. To increase the F/M ratio operators can only control the “M” portion of the equation. By increasing the wasting rate, the MLSS will be reduced causing the F/M ratio to increase.
If the F/M ratio is high, then there is not enough bacteria to consume the large amounts of incoming BOD5. This will lead to poor treatment and the effluent will have a high BOD5 concentration. Operators cannot decrease the amount of BOD5 coming into the plant so they will have to increase the amount of MLSS in the system. They can do this by decreasing or stopping the wasting rate. Decreasing the wasting rate will cause the MLSS to increase and the F/M ratio will be reduced.
The MCRT is another process control tool that is used to determine the wasting rate by manipulating the equation to calculate the MCRT. Often the desired MCRT rate is determined by the design of the treatment facility or from historical data. By taking the pounds of MLSS in the system and dividing it by the desired MCRT, you will determine what the wasting rate needs to be to achieve that MCRT. However, the MCRT and F/M methods for determining the wasting rate can often conflict with each other. Operators need to look at the changes in MCRT and F/M over time and make minor adjustments to the process so the bacteria aren’t “shocked”.
Alternative Process Configurations
There are many different types of process configurations of activated sludge systems that differ by how the wastewater enters the aeration tanks. A plug flow reactor has all of the wastewater and RAS entering at the beginning of the tank. This will have a large organic loading at the beginning of the tank and as the wastewater moves through the tank, the load will lessen. Often, tapered aeration will be used in plug flow reactors. Tapered aeration will have lots of air diffusers at the beginning of the tank so more oxygen is available to the bacteria to handle the increased organic loading. As the wastewater flows through and the BOD5 is reduced, the air diffusers are also reduced.
An alternative is a step feed reactor where the incoming wastewater is split and sent to different portions of the tank. For example, 25% of the flow is sent to the first ¼ of the tank, another 25% to the second ¼ of the tank, and so on. This allows for a more even distribution of the organic loading as well as a more uniform demand for the air diffusers. Typically, a steep feed system will use less air overall than a plug flow reactor.
Secondary Clarification
A secondary clarifier is a key component of the activated sludge system. Not only does it separate out the microorganisms from the now treated wastewater, but it will also concentrate them through the sedimentation process. A secondary clarifier works exactly as discussed previously in primary sedimentation. The only difference is that in a primary sedimentation tank the main goal is to remove unwanted solids. In a secondary sedimentation (or clarifier) tank, the goal is to concentrate the MLSS so it can be returned to the aeration tanks.
How the biomass is settling in the clarifier can be difficult to see in real-time as the tanks are typically below-grade and made of concrete. A “sludge judge” is used to determine how many feet of MLSS are settled on the bottom and how much clear water there is on top. The tool is simply a clear PVC pipe with a ball check valve at the bottom. As the pipe is inserted into the water, the ball check valve opens, letting liquid in. When the stick hits the bottom, the operator will pull the PVC pipe out of the water forcing the ball check to close producing a cross-sectional sample of MLSS on the bottom and clear water on top. There are markings on the PVC pipe for every foot. So as the operator pulls it out of the clarifier, they can see where the clear water stops and where the MLSS is settling. Typically a sludge blanket of 1 to 3 feet on the bottom of the clarifier is optimal.
The settleability of the MLSS can also be seen in the laboratory by taking a sample of the MLSS and putting it into a 1000 mL beaker. After 30-minutes have gone by, the graduations of where the MLSS has settled will be recorded. Dividing the settled sludge volume in mLl/L, dividing by the MLSS in mg/L, and multiplying by 1,000 mg/g will yield the Sludge Volume Index (SVI) in mL/g. The SVI is utilized to gauge how well the MLSS will settle in the clarifier and will also shed light on how the activated sludge plant is operating.
Typical SVI is around 100 to 200 mL/g. Less than 100 mL/g will often show rapid settling of the sludge in the clarifier. When the MLSS settles too quickly, smaller “pin floc” particles will remain suspended in the middle of the clarifier. This will also be seen in the sludge judge test where there is clear water on top of the sludge judge, murky water in the middle, and darker solids on the bottom. This is usually caused by having a higher MCRT. An SVI greater than 200 mL/g will have sludge settling very slowly in the clarifier. This can be caused by having a low MCRT.
The water leaving the secondary clarifier has now gone through all of the previous treatment steps from preliminary screening, to primary sedimentation, and activated sludge treatment. In some areas with less stringent regulations, this water is clean enough to be discharged to the ocean or a nearby waterbody. However, some additional treatment like filtration and disinfection may be needed to meet regulatory compliance. Also, the solids that were removed from the primary and secondary process will still need to be treated and disposed of.


Section 10: Practice Exercises
Practice Exercises
*Part A Provide a justification (rule and line numbers) for each line of proof that requires one.
*Part B Give a proof for each argument in SL.
1. \(K\) & \(L\), .˙. \(K\) ↔ \(L\)
2. \(A\) → (\(B\) → \(C\)), .˙.(\(A\)&\(B\)) → \(C\)
3. \(P\) &(\(Q\)∨\(R\)), \(P\) →¬\(R\), .˙.\(Q\)∨\(E\)
4. (\(C\) & \(D\))∨\(E\), .˙. \(E\)∨\(D\)
5. ¬\(F\) → \(G\), \(F\) → \(H\), .˙. \(G\)∨\(H\)
6. (\(X\) & \(Y\) )∨(\(X\) & \(Z\)), ¬(\(X\) & \(D\)), \(D\)∨\(M\).˙. \(M\)
Part C Give a proof for each argument in SL.
1. \(Q\) → (\(Q\) & ¬\(Q\)), .˙. ¬\(Q\)
2. \(J\) →¬\(J\), .˙. ¬\(J\)
3. \(E\)∨\(F\), \(F\)∨\(G\), ¬\(F\), .˙. \(E\)&\(G\)
4. \(A\) ↔ \(B\), \(B\) ↔ \(C\), .˙. \(A\) ↔ \(C\)
5. \(M\) ∨(\(N\) → \(M\)), .˙. ¬\(M\) →¬\(N\)
6. \(S\) ↔ \(T\), .˙. \(S\) ↔ (\(T\)∨\(S\))
7. (\(M\)∨\(N\))&(\(O\)∨\(P\)), \(N\) → \(P\), ¬\(P\), .˙. \(M\) & \(O\)
8. (\(Z\) & \(K\))∨(\(K\)&\(M\)), \(K\) → \(D\), .˙. \(D\)
Part D Show that each of the following sentences is a theorem in SL.
1. \(O\) → \(O\)
2. \(N\) ∨¬\(N\)
3. ¬(\(P\) &¬\(P\))
4. ¬(\(A\) →¬\(C\)) → (\(A\) → \(C\))
5. \(J\) ↔ [\(J\) ∨(\(L\)&¬\(L\))]
Part E Show that each of the following pairs of sentences are provably equivalent in SL.
1. ¬¬¬¬\(G\), \(G\)
2. \(T\) → \(S\), ¬\(S\) →¬\(T\)
3. \(R\) ↔ \(E\), \(E\) ↔ \(R\)
4. ¬\(G\) ↔ \(H\), ¬(\(G\) ↔ \(H\))
5. \(U\) → \(I\), ¬(\(U\) &¬\(I\))
Part F Provide proofs to show each of the following.
1. \(M\) &(¬\(N\) →¬\(M\)) ⊢ (\(N\) &\(M\))∨¬\(M\)
2. {\(C\) → (\(E\) &\(G\)), ¬\(C\) → \(G\)}⊢ \(G\)
3. {(\(Z\) & \(K\)) ↔ (\(Y\) &\(M\)), \(D\)&(\(D\) → \(M\))}⊢ \(Y\) → \(Z\)
4. {(\(W\) ∨\(X\))∨(\(Y\) ∨\(Z\)), \(X\) → \(Y\), ¬\(Z\)}⊢ \(W\) ∨\(Y\)
Part G For the following, provide proofs using only the basic rules. The proofs will be longer than proofs of the same claims would be using the derived rules.
1. Show that MT is a legitimate derived rule. Using only the basic rules, prove the following: \(\mathcal{A}\)→\(\mathcal{B}\), ¬\(\mathcal{B}\), .˙. ¬\(\mathcal{A}\)
2. Show that Comm is a legitimate rule for the biconditional. Using only the basic rules, prove that \(\mathcal{A}\) ↔\(\mathcal{B}\) and \(\mathcal{B}\) ↔\(\mathcal{A}\) are equivalent.
3. Using only the basic rules, prove the following instance of DeMorgan’s Laws: (¬\(A\)&¬\(B\)), .˙. ¬(\(A\)∨\(B\))
4. Without using the QN rule, prove ¬∃\(x\)¬\(\mathcal{A}\) ⊢∀\(x\)\(\mathcal{A}\)
5. Show that ↔ex is a legitimate derived rule. Using only the basic rules, prove that \(D\) ↔ \(E\) and (\(D\) → \(E\))&(\(E\) → \(D\)) are equivalent.
*Part H
1. Identify which of the following are substitution instances of ∀\(xRcx\): \(Rac\), \(Rca\), \(Raa\), \(Rcb\), \(Rbc\), \(Rcc\), \(Rcd\), \(Rcx\)
2. Identify which of the following are substitution instances of ∃\(x\)∀\(yLxy\): ∀\(yLby\), ∀\(xLbx\), \(Lab\), ∃\(xLxa\)
*Part I Provide a justification (rule and line numbers) for each line of proof that requires one.
*Part J Provide a proof of each claim.
1. ⊢∀\(xFx\)∨¬∀\(xFx\)
2. {∀\(x\)(\(Mx\) ↔ \(Nx\)),\(Ma\)&∃\(xRxa\)}⊢∃\(xNx\)
3. {∀\(x\)(¬\(Mx\)∨\(Ljx\)),∀\(x\)(\(Bx\) → \(Ljx\)),∀\(x\)(\(Mx\)∨\(Bx\))}⊢∀\(xLjx\)
4. ∀\(x\)(\(Cx\)&\(Dt\)) ⊢∀\(xCx\)&\(Dt\)
5. ∃\(x\)(\(Cx\)∨\(Dt\)) ⊢∃\(xCx\)∨\(Dt\)
Part K Provide a proof of the argument about Billy on p. 62.
Part L Look back at Part B on p. 73. Provide proofs to show that each of the argument forms is valid in QL.
Part M Aristotle and his successors identified other syllogistic forms. Symbolize each of the following argument forms in QL and add the additional assumptions ‘There is an \(A\)’ and ‘There is a \(B\).’ Then prove that the supplemented arguments forms are valid in QL.
Darapti:
All \(A\)s are \(B\)s. All \(A\)s are \(C\)s. .˙. Some \(B\) is \(C\).
Felapton:
No \(B\)s are \(C\)s. All \(A\)s are \(B\)s. .˙. Some \(A\) is not \(C\).
Barbari:
All \(B\)s are \(C\)s. All \(A\)s are \(B\)s. .˙. Some \(A\) is \(C\).
Camestros:
All \(C\)s are \(B\)s. No \(A\)s are \(B\)s. .˙. Some \(A\) is not \(C\).
Celaront:
No \(B\)s are \(C\)s. All \(A\)s are \(B\)s. .˙. Some \(A\) is not \(C\).
Cesaro:
No \(C\)s are \(B\)s. All \(A\)s are \(Bs\). .˙. Some \(A\) is not \(C\).
Fapesmo:
All \(B\)s are \(C\)s. No \(A\)s are \(B\)s. .˙. Some \(C\) is not \(A\).
Part N Provide a proof of each claim.
1. ∀\(x\)∀\(yGxy\)⊢∃\(xGxx\)
2. ∀\(x\)∀\(y\)(\(Gxy\) → \(Gyx\))⊢∀\(x\)∀\(y\)(\(Gxy\) ↔ \(Gyx\))
3. {∀\(x\)(\(Ax\) → \(Bx\)),∃\(xAx\)}⊢∃\(xBx\)
4. {\(Na\) →∀\(x\)(\(Mx\) ↔ \(Ma\)),\(Ma\),¬\(Mb\)}⊢¬\(Na\)
5. ⊢∀\(z\)(\(Pz\)∨¬\(Pz\))
6. ⊢∀\(xRxx\) →∃\(x\)∃\(yRxy\)
7. ⊢∀\(y\)∃\(x\)(\(Qy\) → \(Qx\))
Part O Show that each pair of sentences is provably equivalent.
1. ∀\(x\)(\(Ax\) →¬\(Bx\)), ¬∃\(x\)(\(Ax\)&\(Bx\))
2. ∀\(x\)(¬\(Ax\) → \(Bd\)), ∀\(xAx\)∨\(Bd\)
3. ∃\(xPx\) → \(Qc\), ∀\(x\)(\(Px\) → \(Qc\))
Part P Show that each of the following is provably inconsistent.
1. {\(Sa\) → \(Tm\), \(Tm\) → \(Sa\), \(Tm\)&¬\(Sa\)}
2. {¬∃\(xRxa\), ∀\(x\)∀\(yRyx\)}
3. {¬∃\(x\)∃\(yLxy\), \(Laa\)}
4. {∀\(x\)(\(Px\) → \(Qx\)), ∀\(z\)(\(Pz\) → \(Rz\)), ∀\(yPy\), ¬\(Qa\)&¬\(Rb\)}
*Part Q Write a symbolization key for the following argument, translate it, and prove it:
There is someone who likes everyone who likes everyone that he likes. Therefore, there is someone who likes himself.
Part R Provide a proof of each claim.
1. {\(Pa\)∨\(Qb\),\(Qb\) → \(b\) = \(c\),¬\(Pa\)}⊢ \(Qc\)
2. {\(m\) = \(n\)∨\(n\) = \(o\),\(An\)}⊢ \(Am\)∨\(Ao\)
3. {∀\(xx\) = \(m\),\(Rma\)}⊢∃\(xRxx\)
4. ¬∃\(xx\) ≠ \(m\) ⊢∀\(x\)∀\(y\)(\(Px\) → \(Py\))
5. ∀\(x\)∀\(y\)(\(Rxy\) → \(x\) = \(y\)) ⊢ \(Rab\) → \(Rba\)
6. {∃\(xJx\),∃\(x\)¬\(Jx\)}⊢∃\(x\)∃\(y\) \(x\) ≠ \(y\)
7. {∀\(x\)(\(x\) = \(n\) ↔ \(Mx\)),∀\(x\)(\(Ox\)∨¬\(Mx\))}⊢ \(On\)
8. {∃\(xDx\),∀\(x\)(\(x\) = \(p\) ↔ \(Dx\))}⊢ \(Dp\)
9. {∃\(xKx\)&∀\(y\)(\(Ky\) → \(x\) = \(y\))&\(Bx\),\(Kd\)}⊢ \(Bd\)
10. ⊢ \(Pa\) →∀\(x\)(\(Px\)∨\(x\) ≠ \(a)
Part S Look back at Part D on p. 74. For each argument: If it is valid in QL, give a proof. If it is invalid, construct a model to show that it is invalid.
*Part T For each of the following pairs of sentences: If they are logically equivalent in QL, give proofs to show this. If they are not, construct a model to show this.
1. ∀\(xPx\) → \(Qc\), ∀\(x\)(\(Px\) → \(Qc\))
2. ∀\(xPx\)&\(Qc\), ∀\(x\)(\(Px\)&\(Qc\))
3.  If it is invalid, construct a model to show that it is invalid.
1. ∀\(x\)∃\(yRxy\), .˙. ∃\(y\)∀\(xRxy\)
2. ∃\(y\)∀\(xRxy\), .˙. ∀\(x\)∃\(yRxy\)
3. ∃\(x\)(\(Px\)&¬\(Qx\)), .˙. ∀\(x\)(\(Px\) →¬\(Qx\))
4. ∀\(x\)(\(Sx\) → \(Ta\)), \(Sd\), .˙. \(Ta\)
5. ∀\(x\)(\(Ax\) → \(Bx\)), ∀\(x\)(\(Bx\) → \(Cx\)), .˙. ∀\(x\)(\(Ax\) → \(Cx\))
6. ∃\(x\)(\(Dx\)∨\(Ex\)), ∀\(x\)(\(Dx\) → \(Fx\)), .˙. ∃\(x\)(\(Dx\)&\(Fx\))
7. ∀\(x\)∀\(y\)(\(Rxy\)∨\(Ryx\)), .˙. \(Rjj\)
8. ∃\(x\)∃\(y\)(\(Rxy\)∨\(Ryx\)), .˙. \(Rjj\)
9. ∀\(xPx\) →∀\(xQx\), ∃\(x\)¬\(Px\), .˙. ∃\(x\)¬\(Qx\)
10. ∃\(xMx\) →∃\(xNx\), ¬∃\(xNx\), .˙. ∀\(x\)¬\(Mx\)
Part V
1. If you know that \(\mathcal{A}\)⊢\(\mathcal{B}\), what can you say about (\(\mathcal{A}\)&\(\mathcal{C}\))⊢\(\mathcal{B}\)? Explain your answer.
2. If you know that \(\mathcal{A}\)⊢\(\mathcal{B}\), what can you say about (\(\mathcal{A}\)∨\(\mathcal{C}\))⊢\(\mathcal{B}\)? Explain your answer.


6.6: Community Involvement
How Volunteering Can Help You Cultivate a Growth Mindset
Read the article below to consider the impact that volunteering can have on you cultivating a growth mindset:
The Impact of Volunteering on Personal Growth
Volunteering is more than just a way to give back; it also has profound effects on personal growth. Engaging in volunteer work can lead to significant development in various aspects of your life. Here’s a look at how volunteering contributes to personal growth:
1. Enhanced Self-Awareness
Discovering Strengths and Weaknesses: Volunteering often challenges individuals to step outside their comfort zones, leading to a better understanding of their strengths and areas for improvement. Clarifying Values: Working with diverse groups and causes can help clarify personal values and priorities, leading to greater self-awareness and purpose.
2. Improved Emotional Intelligence
Empathy Development: Volunteering allows individuals to connect with people from different backgrounds and situations, fostering empathy and understanding. Emotional Resilience: Facing various challenges and working through them can build emotional resilience, helping you handle stress and adversity better.
3. Enhanced Communication Skills
Interpersonal Skills: Volunteering often involves interacting with diverse individuals, improving your ability to communicate effectively and build relationships. Active Listening: Engaging with people in need teaches active listening skills, helping you understand and respond to others more effectively.
4. Increased Self-Esteem and Confidence
Sense of Accomplishment: Successfully completing volunteer tasks and contributing to meaningful causes boosts self-esteem and confidence in your abilities. Recognition and Feedback: Positive feedback and recognition from those you help can further enhance your self-worth and confidence.
5. Expanded Professional Skills
Skill Development: Volunteering provides opportunities to develop and refine skills such as project management, teamwork, and problem-solving, which can be valuable in professional settings. Networking Opportunities: Connecting with professionals and fellow volunteers can open doors to new career opportunities and provide valuable contacts in your field.
6. Broadened Perspectives
Cultural Awareness: Volunteering with diverse groups exposes you to different cultures, viewpoints, and lifestyles, broadening your perspective and increasing cultural sensitivity. Understanding Social Issues: Working on various projects helps you gain a deeper understanding of social issues and challenges faced by different communities.
7. Increased Sense of Purpose
Finding Meaning: Contributing to causes you care about provides a sense of purpose and fulfillment, helping you align your actions with your values. Goal Setting: Volunteer work often involves setting and achieving goals, which can enhance your sense of direction and motivation in both personal and professional life.
8. Development of Leadership Skills
Taking Initiative: Volunteering can provide opportunities to lead projects, manage teams, and take initiative, helping you develop and refine leadership skills. Decision-Making: Making decisions and solving problems in a volunteer setting can enhance your decision-making abilities and confidence in leadership roles.
9. Strengthened Problem-Solving Abilities
Creative Solutions: Volunteering often involves tackling challenges with limited resources, fostering creativity and innovative problem-solving skills. Adaptability: Navigating unexpected situations and adapting to changing needs improves your ability to think on your feet and handle complex problems.
10. Fostering a Growth Mindset
Embracing Learning: Volunteering encourages a growth mindset by presenting opportunities for continuous learning and personal development. Resilience Building: Facing and overcoming challenges in volunteer work fosters resilience and a positive attitude towards personal growth and change.
11. Enhanced Teamwork Skills
Collaboration: Working with others towards a common goal enhances your ability to collaborate effectively and understand different team dynamics. Conflict Resolution: Volunteering in diverse teams can teach you valuable skills in managing and resolving conflicts, promoting a positive team environment.
12. Increased Community Engagement
Connecting with Others: Volunteering helps you build connections with your community and engage more deeply in local issues and initiatives. Building Relationships: Forming relationships with fellow volunteers and community members enriches your social network and sense of belonging.
Conclusion
Volunteering offers a wealth of benefits for personal growth, including enhanced self-awareness, improved emotional intelligence, and increased confidence. By providing opportunities for skill development, broadening perspectives, and fostering a sense of purpose, volunteering plays a crucial role in shaping and enriching your personal development journey. Embrace the opportunity to grow both personally and professionally through meaningful volunteer experiences.
Journal Assignment
After reading the above, take some time to consider each of the questions below and document your thoughts:
1. How do you think volunteering could help you identify areas for personal improvement?
2. What skills do you want to develop for your future career? How could community service help you to gain hands-on experience in those areas?
3. How comfortable are you with adapting to unexpected challenges? How do you think community involvement could help you improve your adaptability?
4a. Identify 3 community service (volunteering) activities you would be interested in pursuing.
4b. Explain why each option interests you and how it would promote a growth mindset for YOU .