GATE | GATE CS 2019 | Question 41

Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas and Z where Y = (PR) and Z = (QRS). Consider the two statements given below:

• I. Both Y and Z are in BCNF
• II. Decomposition of X into Y and Z is dependency preserving and a lossless.

Which of the above statements is/are correct?

(A)

I only

(B)

Neither I nor II

(C)

Both I and II

(D)

II only

Answer: (D)

Explanation:

X(PQRS) {QR → S, R → P, S → Q} decomposed into Y (PR) and Z (QRS). So,

Y (PR)	Z (QRS)
{R → P}  Candidate key : {R}  So, relation Y in BCNF	{QR → S, S → Q}  Candidate key : {QR, RS}  So, relation Z in 3NF but not BCNF, becasuse of S is not superkey.

Since, this decomposition covers all functional dependencies of original relation (X), so decomposition of X into Y and Z is dependency preserving. Also, this decomposition has common attribute (i.e., R) which is superkey of relation Y(PR), so decomposition of X into Y and Z is also lossless join decomposition. Option (D) is correct.

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