Open In App

GATE | GATE CS 2019 | Question 41

Like Article
Like
Save
Share
Report

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.


Quiz of this Question
Please comment below if you find anything wrong in the above post


Last Updated : 26 Feb, 2019
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads