Answer key to CSC4402 Homework#5

HOMEWORK > Answer key to CSC4402 Homework#5

Louisiana State University CSC 4402 Answer key to CSC4402 Homework#5 Due Monday November 13, 2006 1. Question 6.2 in the text book (page 256). (I skip this one - the answer key is actually in the book author’s website) 2. Shown below is a relation value (instance) for the relation variable r(R) where the relation schema R is giv en by R(A ...[Show More]

Louisiana State University
CSC 4402
Answer key to CSC4402 Homework#5 Due Monday November 13, 2006

1. Question 6.2 in the text book (page 256).

(I skip this one - the answer key is actually in the book author’s website)

2. Shown below is a relation value (instance) for the relation variable r(R) where the relation schema

R is giv en by R(ABCDE).

Relation value for r(R)

A B C D E

A1 B1 C1 D1 E1

A1 B2 C1 D1 E1

A2 B2 C1 D2 E3

A2 B3 C3 D2 E2

Consider the set of functional dependencies F = {A → B, B → C, D → E, CD → E}.

(a) For each functional dependency (fd) in F, determine whether or not this fd is satisfied by this

relation value for r(R). Briefly explain your answer for each fd (why the fd is satisfied (or not)

by this relation value).

Answer:

A → B.

This functional dependency is NOT satisfied by this relation value for r(R) because we have

tuples with the same value for attribute A but different values for attribute B. For example, the

first two tuples have A = A1, these two tuples have different values (B1 and B2 respectively) for

attribute B.

B → C.

This functional dependency is satisfied by this relation value for r(R). This is because the

tuples (the 2nd and 3rd tuples) that have the same value (B2) for attribute B also have the same

value C1) for attribute C.

D → E.

This functional dependency is NOT satisfied by this relation value for r(R) because (similar to

the case of A → B) this relation value has two tuples with the same value for attribute D but

different values for attribute E. Namely, the value D2 for attribute D is associated with two different values E2 and E3 in r.

CD → E.

This functional dependency is satisfied by this relation value for r(R). This is because the

tuples (the 1st and the 2nd tuples) with the same value for attributes C and D (C1 and D1) hav e

the same value for attribute E (E1).

(b) Note that the relation variable r(R) can have many diff