title: Understanding 3NF: plain English please
body: <p>I am working through an example problem in which we are trying to identify which of the following relations is in Third Normal Form (3NF). Here are the relations we are given:</p>
  
  <p><strong>R1(ABCD)<br>
  ACD -> B &emsp; AC -> D &emsp; D -> C &emsp; AC -> B</strong></p>
  
  <p>R2(ABCD)<br>
  AB -> C &emsp; ABD -> C &emsp; ABC -> D &emsp; AC -> D</p>
  
  <p>R3(ABCD)<br>
  C -> B &emsp; A -> B &emsp; CD -> A &emsp; BCD -> A</p>
  
  <p>R4(ABCD)<br>
  C -> B &emsp; B -> A &emsp; AC -> D &emsp; AC -> B</p>
  
  <p>I know the answer is R1 is in 3NF, but I'm having a hard time understanding the steps to go about determining what violates 3NF. Can someone break it down in plain English for each of the relations? It would be extremely helpful if you can show me in steps how each relation might violate one of the 3NF rules:</p>
  
  <ol>
  <li>X -> A, then A is a subset of X</li>
  <li>X is a superkey</li>
  <li>A is a part of some key for R</li>
  </ol>
  
  <p>For R1, the first step I take is breaking it down into closures:</p>
  
  <p>ACD+ = ABCD<br>
  AC+ = ABCD<br>
  D+ = C</p>
  
  <p>ACD and AC are superkeys, which satisfy rule 2.<br>
  1. D -> C, but C is not a subset of D. Rule 1 violated.<br>
  2. D is not a superkey. Rule 2 is violated.<br>
  3. C is a part of some key for R. C is a part of AC and ACD. So, rule 3 is upheld?  </p>
  
  <p>Not sure if I'm even doing these steps right, so please break it down as simple as possible for someone struggling with these concepts. Thanks.</p>