Question

Consider the relation X(P, Q, R, S, T, U) with the following set of functional dependencies

                F = {

                                {P, R} → {S, T},

                                {P, S, U} → {Q, R}

                         }

Which of the following is the trivial functional dependency in F⁺, where F⁺ is closure of F?

1. {P, R} → {S, T}
2. {P, R} → {R, T}
3. {P, S} → {S}
4. {P, S, U} → {Q}

Answer 1

Correct Answer - Option 3 : {P, S} → {S}

Concept:

The closure of F, denoted as F+, is the set of all regular FD, that can be derived from.

For trivial functional dependency,

Let A and be two sets consists of attributes of a relation

A → B

A \(\supseteq\) B 

Explanation:

Option 1: 

{P, R} → {S, T}

{P, R} \(\nsupseteq\) {S, T}

Not a trivial functional dependency

Option 2: 

{P, R} → {R, T}

{P, R} \(\nsupseteq\) {R, T}

Not a trivial functional dependency

Option 3: 

{P, S} → {S}

{P, S} \(\supseteq\) {S}

It is a trivial functional dependency

Option 4: 

{P, S, U} → {Q}

{P, S, U} \(\nsupseteq\) {Q}

Not a trivial functional dependency

NOTE:

\(\supseteq\) → superset

\(\nsupseteq\) → not superset