Question

Suppose relation R(A,B,C,D,E), and set of FD's S={ A->B, B->D, AD->C }. Find one key of R.

Select one:
a. {A}
b. {A,B,E}
c. {B,E}
d. {A,E}

Answer 1

The key for the relation R with the given functional dependencies is {A,E}. The attributes A and E together can determine all other attributes in the relation, making AE a candidate key.

Step-by-step explanation:

The student has asked for a key of the relation R(A,B,C,D,E) with a given set of functional dependencies S={A->B, B->D, AD->C}. To find a key, we need to determine the attributes that uniquely identify a tuple in R. We start with the attributes on the left side of the functional dependencies, which are A and B (from A->B), and AD (from AD->C).

A cannot be a key by itself because from A we can find B and D (using B->D), but not C and E. However, if we augment A with E (AE), we can find B from A, then D from B, and additionally, if we have A and D, we can find C using AD->C. Hence, AE can determine B, D, and C, and it already includes E, so all attributes in R are covered.

Therefore, the answer is d. {A,E}, as AE is a candidate key for the relation R.