Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.(a) R = {(1, 2), (1, 3), (1, 4)}(b) R = {(1, 2), (2, 1)}(c) R = {(1, 1), (2, 2), (3, 3)}(d) R = {(1, 1), (1, 2), (2, 3)}The question was asked in examination.Question is from Types of Relations in section Relations and Functions of Mathematics – Class 12

Which of the following relations is symmetric but neither reflexive no

1.	Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.(a) R = {(1, 2), (1, 3), (1, 4)}(b) R = {(1, 2), (2, 1)}(c) R = {(1, 1), (2, 2), (3, 3)}(d) R = {(1, 1), (1, 2), (2, 3)}The question was asked in examination.Question is from Types of Relations in section Relations and Functions of Mathematics – Class 12
Answer» Right choice is (b) R = {(1, 2), (2, 1)} Easy explanation: A RELATION in a set A is said to be symmetric if (A1, a2)∈R implies that (a1, a2)∈R,for every a1, a2∈R. Hence, for the given set A={1, 2, 3}, R={(1, 2), (2, 1)} is symmetric. It is not reflexive since every element is not related to itself and neither transitive as it does not satisfy the condition that for a given 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.

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