UGC NET CSE | December 2015 | Part 2 | Question: 20

Question

A relation R={A,B,C,D,E,F,G} is given with following set of functional dependencies: F={AD→E, BE→F, B→C, AF→G}. Which of the following is a candidate key?

• A. A
• B. AB
• C. ABC
• D. ABD

Answer 1

Given Relation is R = ABCDEFG

Take options

1. A = A
2. AB = ABC
3. ABC = ABC
4. ABD = ABDEFCG (ABCDEFG)

Hence answer would be 4) ABD will be the candidate keys. 

Answer 2

ABD={A,B,C,D,E,F,G} Simply take  closure of ABD .

Answer 3

Find the closure of each options given

answer is ABD

ABD+  = initially add {A,B,D}

since AD -> E we can add E

then since BE -> F we can add F also

so ABD+ = {A,B,C,D,E,F}

since the closure contain all the attributes in the relation. it is a candidate key

for other options the attribute closure will not contain all the attributes