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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 Y 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 lossless
Which of the above statements is/are correct?
  • a)
    Both I and II
  • b)
    I only
  • c)
    II only
  • d)
    Neither I nor II
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let the set of functional dependencies F = {QR → S, R → P, S...
X = (PQRS)
Set of functional dependencies
F = {QR → S, R → P, S → Q}
QR → {Q, R, S, P}
SR → {S, R, P, Q}
QR and SR are keys of Relation schema X
R → P …
part of key (R) → non key(P)
It is partial dependency and hence not in 2nd normal form and therefore not in BCNF (Given)
X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS)
For Y = (PR)
R → P
Y is in BCNF because binary attribute (R is a key).
For Z = (QRS)
QR → S
S → Q
SR → {R, S, Q}
QR → {R, Q, S}
QR and SR are keys of Relation schema X
Z is not in BCNF because
S → Q and S is not Super key.
∴ statement I is incorrect
Dependency Preserving:
R → P is in Y
QR → S in Z
S → Q is in Z
Hence, it is dependency preserving.
Lossless:
Y ∩ Z = R which is key of Y.
Therefore, it is Lossless
Statement II is correct.
Hence, option 3 is the answer
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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 Y and Z, where Y = (PR) and Z = (QRS).Consider the two statements given below.I. Both Y and Z are in BCNFII. Decomposition of X into Y and Z is dependency preserving and losslessWhich of the above statements is/are correct?a)Both I and IIb)I onlyc)II onlyd)Neither I nor IICorrect answer is option 'C'. Can you explain this answer?
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