Question

Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?

(a) R = {(7, 7), (8, 8), (9, 9)}

(b) R = {(7, 8), (8, 7), (8, 9)}

(c) R = {0}

(d) R = {(7, 8), (8, 8), (8, 9)}

This question was addressed to me during an interview.

This key question is from Types of Relations in section Relations and Functions of Mathematics – Class 12

Answer 1

Correct option is (a) R = {(7, 7), (8, 8), (9, 9)}

Easy explanation: The relation R= {(7, 7), (8, 8), (9, 9)} is reflexive as every element is related to itself i.e. (a,a) ∈ R, for every a∈A. and it is not transitive as it does not satisfy the condition that for a relation R in a set A if (a1, a2)∈R and (a2, a3)∈R implies that (a1, a3) ∈ R for every a1, a2, a3 ∈ R.