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
• B. symmetric
• C. transitive
• D. an equivalence relation

Answer 1

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,
$\therefore$ R is symmetric
Also.(1, 2) and (2, 1) $ϵ$ R $\Rightarrow$ (1, 1) $ϵ$ R.
Similarly, for other elements, hence R is transitive,
$\therefore$ R is equivalence relation.