Question

(a1, a2) ∈R implies that (a2, a1) ∈ R, for all a1, a2∈A. This condition is for which of the following relations?

(a) Equivalence relation

(b) Reflexive relation

(c) Symmetric relation

(d) Universal relation

This question was posed to me by my school principal while I was bunking the class.

Query is from Types of Relations topic in section Relations and Functions of Mathematics – Class 12

Answer 1

The correct option is (c) Symmetric relation

The best I can explain: The above is a condition for a symmetric relation.

For example, a relation R on set A = {1,2,3,4} is given by R={(a,b):a+b=3, a>0, b>0}

1+2 = 3, 1>0 and 2>0 which implies (1,2) ∈ R.

Similarly, 2+1 = 3, 2>0 and 1>0 which implies (2,1)∈R. Therefore both (1, 2) and (2, 1) are converse of each other and is a part of the relation. Hence, they are symmetric.