Question

Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?

(a) R = {(4, 4), (5, 4), (5, 5)}

(b) R = {(4, 4), (5, 5)}

(c) R = {(4, 5), (5, 4)}

(d) R = {(4, 5), (5, 4), (4, 4)}

The question was posed to me in an internship interview.

The origin of the question is Types of Relations in chapter Relations and Functions of Mathematics – Class 12

Answer 1

Correct answer is (d) R = {(4, 5), (5, 4), (4, 4)}

For explanation: R= {(4, 5), (5, 4), (4, 4)} is symmetric since (4, 5) and (5, 4) are converse of each other thus satisfying the condition for a symmetric relation and it is transitive as (4, 5)∈R and (5, 4)∈R implies that (4, 4) ∈R. It is not reflexive as every element in the set I is not related to itself.