Suppose the following functional dependencies hold on a relation U with…
2021
Suppose the following functional dependencies hold on a relation U with attributes P,Q,R,S, and T:
P → QR
RS → T
Which of the following functional dependencies can be inferred from the above functional dependencies?
- A.
PS → T
- B.
R → T
- C.
P → R
- D.
PS → Q
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Correct answer: A, C, D
Short answer: The inferred functional dependencies are PS → T, P → R, and PS → Q. R → T cannot be inferred.
Reasoning (closure calculations):
Closure of P: start with {P}. Using P → Q R add Q and R, so P+ = {P, Q, R}. Therefore P → R and P → Q hold.
Closure of PS: start with {P, S}. From P → Q R add Q and R, giving {P, S, Q, R}. Then apply R S → T to add T, so PS+ contains T. Thus PS → T. Also since P → Q, PS → Q holds as well.
Why R → T is not inferred: R S → T requires S in addition to R. R alone does not provide S, so you cannot derive T from R by itself. Hence R → T does not follow from the given dependencies.
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