### CS 4250: Database Management Systems

#### Due Thursday, 4/20/2017, at midnight

This is an individual assignment. All work must be your own. You should not look at any other student's work (in whole or in part, on paper or on screen), nor allow anyone else to look at yours, during the course of this assignment.

You may email a plain text, MS Word or PDF document to the instructor with subject line "cs4250,hw3" (by midnight), or turn in a typed hardcopy (during class time on 4/??).

1. Consider a relation R with attributes ABCDEF. You are given the following dependencies A -> C, D -> E, BC -> D.

1. Attribute closure of A?

2. Attribute closure of B?

3. Attribute closure of BC?

4. Attribute closure of AB?

5. Attribute closure of DF?

6. Identify which, if any, of the above are candidate keys.

2. Consider a relation R with attributes ABCDE. You are given the following dependencies CE -> A, CE -> B, CE -> D, B -> C

1. List all (candidate) keys for R.

2. Is R in 3NF? Why or why not?

3. Is R in BCNF? Why or why not?

3. Consider a relation R with attributes ABCDE. You are given the following dependencies AB -> D, AB -> E, A -> C.

1. List all (candidate) keys for R.

2. Is R in 3NF? Why or why not?

3. Is R in BCNF? Why or why not?

4. Suppose that we have the following three tuples in a legal instance of a relation schema S with attributes primary_key, A, B and C:
attribute namesprimary_keyA B C
tuple 114 1 4
tuple 228 1 4
tuple 336 2 5

1. For each of the following dependencies, can you infer whether or not it holds over schema S? Why or why not?
1. A -> C

2. C -> A

2. Can you identify any functional dependencies that hold over S? If so, please name one.

5. Suppose you are given a relation R(A, B, C, D). For each of the following sets of FDs, assume they are the only dependencies that hold for R. Do the following: a) identify the candidate key(s) for R. b) State whether or not the proposed decomposition of R into smaller relations is a good decomposition and briefly explain why or why not.

1. A -> D, D -> C; decompose into AD and BC.
1. Candidate keys:
2. Analysis:

2. A -> BC, B -> D; decompose into ABC and BD.
1. Candidate keys:
2. Analysis:

3. A -> B, B -> C, C -> D; decompose into AB, AD and CD.
1. Candidate keys:
2. Analysis:

4. A -> B, B -> C, C -> D; decompose into ABC and BCD.
1. Candidate keys:
2. Analysis:

5. B -> AD, D -> BC; decompose into ABD and BC.
1. Candidate keys:
2. Analysis:

6. Suppose you are given a relation R with attributes ABCDEF. You are given functional dependencies A -> D, BC -> F, and D -> C. Using the decomposition techniques described in class, decompose this relation into relations in "good" normal forms. For each of the new relations you create, identify the normal form it is in.

If you choose not to decompose the relations into the best normal form we discussed, explain why you made that choice. If there are any interesting issues or potential problems with your decomposition, explain what they are.