GATE CS 2021 Set 2 — Question 50
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Databases → Normalization → Armstrong's Axioms
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Question
Suppose the following functional dependencies hold on a relation with attributes and :
P → QRRS → TWhich of the following functional dependencies can be inferred from the above functional dependencies?Correct answer
(A) PS arrow T; (C) P arrow R; (D) PS arrow Q
Solution
Given functional dependencies (FDs):
From
Since
From
From
1.
P → QR2.
From FD 1, using the decomposition rule, we can infer:RS → TP → QP → R(This makes option (C) correct)
PS → T:From
P → R, by augmentation with , we get PS → RS.Since
PS → RS and RS → T (FD 2), by transitivity, we get PS → T. (This makes option (A) correct)Now, consider PS → Q:From
P → Q, by augmentation with , we get PS → QS.From
PS → QS, by decomposition, we get PS → Q. (This makes option (D) correct)Option (B) R → T cannot be inferred because we only know that is functionally dependent on the combination of and , not on alone.Continue learning with Success Tracker
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