Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a and b are elements of a group and a is not equal to b, then a^2 is not equal to b^2. Statement 2 | The set of rotations in a dihedral group form a cyclic subgroup.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | In a group (ab)^{-2} = b^{-2}a^{-2}. Statement 2 | In a group (ab)^n = a^nb^n.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | S_n is non-Abelian for all n >= 3. Statement 2 | If a is a permutation that is an m-cycle and b is a permutation that is an n-cycle, then |ab| = lcm(m,n).
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find the characteristic of the ring Z x Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the characteristic of the ring Z x Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the characteristic of the ring Z x Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer:


Question: Find the characteristic of the ring Z x Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the characteristic of the ring Z x Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer:


Question: Find the characteristic of the ring Z x Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the characteristic of the ring Z x Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer:


Question: Find the characteristic of the ring Z x Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the characteristic of the ring Z x Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer:


Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If K is a nonzero subgroup of a finitely generated free abelian group, then K is free abelian. Statement 2 | If K is a nonzero subgroup of a finitely generated free abelian group, then G / K is free abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | The external direct product of cyclic groups is cyclic. Statement 2 | The external direct product of D_3 and D_4 is isomorphic to D_12.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).
 A. -19
 B. -10
 C. 19
 D. 10
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).
 A. -19
 B. -10
 C. 19
 D. 10
Answer:


Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).
 A. -19
 B. -10
 C. 19
 D. 10
Answer:


Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).
 A. -19
 B. -10
 C. 19
 D. 10
Answer:


Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).
 A. -19
 B. -10
 C. 19
 D. 10
Answer:


Question: Compute the product in the given ring. (12)(16) in Z_24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (12)(16) in Z_24
 A. 0
 B. 1
 C. 4
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Compute the product in the given ring. (12)(16) in Z_24
 A. 0
 B. 1
 C. 4
 D. 6
Answer:


Question: Compute the product in the given ring. (12)(16) in Z_24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (12)(16) in Z_24
 A. 0
 B. 1
 C. 4
 D. 6
Answer:


Question: Compute the product in the given ring. (12)(16) in Z_24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (12)(16) in Z_24
 A. 0
 B. 1
 C. 4
 D. 6
Answer:


Question: Compute the product in the given ring. (12)(16) in Z_24

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Compute the product in the given ring. (12)(16) in Z_24
 A. 0
 B. 1
 C. 4
 D. 6
Answer:


Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find all cosets of the subgroup 4Z of 2Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all cosets of the subgroup 4Z of 2Z.
 A. 4Z
 B. 4Z, 2 + 4Z
 C. 2Z
 D. Z
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find all cosets of the subgroup 4Z of 2Z.
 A. 4Z
 B. 4Z, 2 + 4Z
 C. 2Z
 D. Z
Answer:


Question: Find all cosets of the subgroup 4Z of 2Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all cosets of the subgroup 4Z of 2Z.
 A. 4Z
 B. 4Z, 2 + 4Z
 C. 2Z
 D. Z
Answer:


Question: Find all cosets of the subgroup 4Z of 2Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all cosets of the subgroup 4Z of 2Z.
 A. 4Z
 B. 4Z, 2 + 4Z
 C. 2Z
 D. Z
Answer:


Question: Find all cosets of the subgroup 4Z of 2Z.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all cosets of the subgroup 4Z of 2Z.
 A. 4Z
 B. 4Z, 2 + 4Z
 C. 2Z
 D. Z
Answer:


Question: Which of the following statements is true?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Which of the following statements is true?
 A. Every equivalence relation is a partial-ordering relation.
 B. Number of relations form A = {x, y, z} to B= (1, 2), is 64.
 C. Empty relation _ is reflexive
 D. Properties of a relation being symmetric and being un-symmetric are negative of each other.
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Which of the following statements is true?
 A. Every equivalence relation is a partial-ordering relation.
 B. Number of relations form A = {x, y, z} to B= (1, 2), is 64.
 C. Empty relation _ is reflexive
 D. Properties of a relation being symmetric and being un-symmetric are negative of each other.
Answer:


Question: Which of the following statements is true?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Which of the following statements is true?
 A. Every equivalence relation is a partial-ordering relation.
 B. Number of relations form A = {x, y, z} to B= (1, 2), is 64.
 C. Empty relation _ is reflexive
 D. Properties of a relation being symmetric and being un-symmetric are negative of each other.
Answer:


Question: Which of the following statements is true?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Which of the following statements is true?
 A. Every equivalence relation is a partial-ordering relation.
 B. Number of relations form A = {x, y, z} to B= (1, 2), is 64.
 C. Empty relation _ is reflexive
 D. Properties of a relation being symmetric and being un-symmetric are negative of each other.
Answer:


Question: Which of the following statements is true?

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Which of the following statements is true?
 A. Every equivalence relation is a partial-ordering relation.
 B. Number of relations form A = {x, y, z} to B= (1, 2), is 64.
 C. Empty relation _ is reflexive
 D. Properties of a relation being symmetric and being un-symmetric are negative of each other.
Answer:


Question: Find the maximum possible order for an element of S_n for n = 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 6.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the maximum possible order for an element of S_n for n = 6.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 6.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 6.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Find the maximum possible order for an element of S_n for n = 6.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the maximum possible order for an element of S_n for n = 6.
 A. 6
 B. 12
 C. 30
 D. 105
Answer:


Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2
 A. 0
 B. 1
 C. 0,1
 D. 2
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2
 A. 0
 B. 1
 C. 0,1
 D. 2
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2
 A. 0
 B. 1
 C. 0,1
 D. 2
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2
 A. 0
 B. 1
 C. 0,1
 D. 2
Answer:


Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2
 A. 0
 B. 1
 C. 0,1
 D. 2
Answer:


Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.
 A. 25
 B. 5
 C. 6
 D. 30
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.
 A. 25
 B. 5
 C. 6
 D. 30
Answer:


Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.
 A. 25
 B. 5
 C. 6
 D. 30
Answer:


Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.
 A. 25
 B. 5
 C. 6
 D. 30
Answer:


Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Find the number of elements in the indicated cyclic group: The cyclic subgroup of Z_30 generated by 25.
 A. 25
 B. 5
 C. 6
 D. 30
Answer:


Question: The element (4, 2) of Z_12 x Z_8 has order

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The element (4, 2) of Z_12 x Z_8 has order
 A. 4
 B. 8
 C. 12
 D. 6
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: The element (4, 2) of Z_12 x Z_8 has order
 A. 4
 B. 8
 C. 12
 D. 6
Answer:


Question: The element (4, 2) of Z_12 x Z_8 has order

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The element (4, 2) of Z_12 x Z_8 has order
 A. 4
 B. 8
 C. 12
 D. 6
Answer:


Question: The element (4, 2) of Z_12 x Z_8 has order

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The element (4, 2) of Z_12 x Z_8 has order
 A. 4
 B. 8
 C. 12
 D. 6
Answer:


Question: The element (4, 2) of Z_12 x Z_8 has order

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: The element (4, 2) of Z_12 x Z_8 has order
 A. 4
 B. 8
 C. 12
 D. 6
Answer:


Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:

Context:
The following are multiple choice questions (with answers) about abstract algebra.

Question: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
 A. 0
 B. 1
 C. 2
 D. 3
Answer: B

Question: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: B

Question: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: C

Question: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: A

Question: Find the characteristic of the ring 2Z.
 A. 0
 B. 3
 C. 12
 D. 30
Answer: A

Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer:


Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.

abstract_algebra

Choices:
- A
- B
- C
- D

Question:
Question: Statement 1 | Every ideal in a ring is a subring of the ring. Statement 2 | Every subring of every ring is an ideal of the ring.
 A. True, True
 B. False, False
 C. True, False
 D. False, True
Answer: