GATE CSE 2021 | Set 2 | Question: 40

Question

Suppose the following functional dependencies hold on a relation $U$ with attributes $P,Q,R,S$, and $T$:

• $P \rightarrow QR$
• $RS \rightarrow T$

Which of the following functional dependencies can be inferred from the above functional dependencies?

• A. $PS \rightarrow T$
• B. $R \rightarrow T$
• C. $P \rightarrow R$
• D. $PS \rightarrow Q$

Comments

Closure operation works

Answer 1

Option A: $(PS)^+ = {P, Q, R, S, T}.$ So, $PS\rightarrow T$ holds.

Option B: $(R)^+ = {R}.$ So, $R\rightarrow T$ does not hold.

Option C: $(P)^+ = {P, Q, R}.$ So, $P\rightarrow R$ holds.

Option D: $(PS)^+ = {P, Q, R, S, T}.$ So, $PS\rightarrow Q$ holds.

Comments

So option A, C and D are inferred  or concluded TRUE from the given FD.

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Given : 

P → QR

RS  → T

we can apply the decomposition rule for  P → QR  it gives P → Q and P → R which satisfies option C.

For all remaining, we can follow the closure property Rule.

Answer 2

Check for the reachability using the Closer operation...

Answer 3

Option A , C and D can be inferred true from the given FD.

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