## Homework Assignment 3

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CS 430: Database Management Systems

* Due Date - 11:59PM Sunday, February 25*^{th}

*NO LATE PERIOD*

^{th}

*NO LATE PERIOD*

### Homework Assignment 3

* Each question is worth 25 points. *

- Consider a relation R with five attributes ABCDE. You are given the
following dependencies: A → B, BC → E, and ED → A.
- List all keys for R.
- Is R in 3NF?
- Is R in BCNF?

- Consider the following collection of relations and dependencies. Assume
that each relation is obtained through decomposition from a relation with attributes
ABCDEFGHI and that all the known dependencies over relation ABCDEFGHI
are listed for each question. (The questions are independent of each other.)
For each (sub)relation: (1) State the strongest normal form that the relation is in. (2) If it is not in BCNF, decompose it into a collection of BCNF relations.

- R1(A,C,B,D,E), A → B, C → D
- R2(A,B,F), AC → E, B → F
- R3(A,D,G), D → G, G → H
- R4(D,C,H,G), A → I, I → A
- R5(A,I,C,E)

- Suppose that we pick the following three tuples from a legal instance of
a relation S (S has 100 tuples in total). Relation S has the following schema:
(A : integer, B : integer, C : integer).

The three tuples are: (1,2,3), (4,2,3), and (5,3,3).

- Which of the following dependencies can you infer does not hold over S?
- A → B,
- BC → A,
- C → B

- Can you identify any dependencies that hold over S?

- Which of the following dependencies can you infer does not hold over S?
- Suppose that we pick the following four tuples from a legal relation S
(S has 100 tuples in total). S has the following schema:
(A: integer, B: integer, C: integer)

The four tuples are: (1,2,3), (4,2,3), (5,3,3) and (5,3,4).

Which of the following functional (→)can you infer does not hold over relation S?

- A → B
- BC → A
- A → C
- AC → B

**These homework solutions must be checked into Canvas in .pdf format**

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