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

Which of the following relations is symmetric and transitive but not r

1.	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» 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.

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