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(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 relationThis 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»

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.


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