Question

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 1

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.