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Question

Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is

A
Reflexive
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B
symmetric
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C
transitive
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D
an equivalence relation
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Solution

The correct option is D an equivalence relation
R = {(1, 1) (2, 2) (3, 3) (4, 4) (1, 2) (2, 1) (3, 1) (1, 3)}
As (1, 1), (2, 2), (3, 3), (4, 4) ϵ R is reflexive
(1, 2) and (2, 1) ϵ R, also (3, 1) and (1, 3) ϵ R,
R is symmetric
Also.(1, 2) and (2, 1) ϵ R (1, 1) ϵ R.
Similarly, for other elements, hence R is transitive,
R is equivalence relation.

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