Question

Let A = {1, 2, 3, 4} and R = {(1, 2),(2, 3), (1, 4)} be a relation on A. Let S be the equivalence relation on A such that R \(\subset\) S and the number of elements in S is n. Then, the minimum value of n is ______.

Answer 1

Correct answer: 16

A = {1, 2, 3, 4}

R = {(1, 2) (2, 3) (1, 4)}

For equivalence relation, relation must be reflexive, symmetric & transitive

R = {(1, 1) (2, 2) (3, 3)(4, 4) (1, 2) (2,1) (2,3)

(3, 2) (1, 4) (4, 1) (1, 3) (3, 1) (2, 4) (4, 2) (4, 3) (3, 4)}

All elements are included

\(\therefore\) Answer is 16.