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 Tuesday Nov. 13, 2018 1. Shown below is a relation instance for the relation R with relation schema R(ABCDE). Relation instance 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 A2 B3 C3 D4 E2 Co ...[Show More]

Louisiana State University
CSC 4402
Answer Key to CSC4402 Homework 5 Due Tuesday Nov. 13, 2018

1. Shown below is a relation instance for the relation R with relation schema R(ABCDE).

Relation instance 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

A2 B3 C3 D4 E2

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

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

instance for R. Briefly explain your answer for each fd (why the fd is satisfied (or not) by this relation

instance).

Answer:

A → B.

This functional dependency is NOT satisfied by this relation instance because we have tuples with the

same value for attribute A but different values for attribute B. For example, the first and second tuples have

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

BC → D.

This functional dependency is NOT satisfied by this relation instance: The second and third tuples have B=

B2 and C= C1, but the associated D values are NOT the same for these two tuples (D1 and D2).

D → E.

This functional dependency is NOT satisfied by this relation instance because this relation instance 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 for attribute E.

CD → E.

This functional dependency is satisfied by this relation instance. 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).

2. Let R(ABC) be a relation with attributes A, B and C. Let F1 and F2 be sets of functional dependencies where F1 ={ A → B, A → C } and F2 ={A → B, B → C}.

(Here to get some intuitions about the relation R, you may think of R as representing information

about a person - attribute A represents the SSN of the person, attribute B represents the address of the

person, and attribute C represents the phone number of the person. However, this visualization of R

should NOT impact your answers to the question)

(2.1) Compute F1+, F2+ (using the compact representation we discussed in class). Is F1 equivalent to

F2 ? Explain your answer.