GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 41

Which of the following set of functional dependencies of relation R (ABCD) is not in 3NF ?
(A) { AB → C, D → B, AC → D }
(B) { C → B, A → B, CD → A, BCD → A }
(C) { C → D, CD →A, AB →C, BD →A }
(D) None of these


Answer: (B)

Explanation:
(A): This relation has 3 candidate keys: {AB, AC, and AD}. Since all are prime attributes, so relation is in 3 NF.
(B): {CD} is the only candidate key of R, since {CD}+ ={ABCD}. R is not in 3NF, since FDs C → B and A → B violate this normal form.
(C): This relation has 3 candidate keys: {BC, BD and BA}. Since all are prime attributes, so relation is in 3 NF.

Option (B) is correct.

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