Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.

Question

Philoid · Accepted Answer

It is given that the relation in the set {1, 2, 3, 4} given by

R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)}

It is seen that (a, a) ϵ R, for every a ϵ {1,2,3,4}

Therefore, R is reflexive.

We can seen that (1, 2) ϵ R, but (2, 1) ∉R.

Therefore, R is not symmetric.

Also, it is clear that (a, b), (b, c) ϵ R

⇒ (a, c) ϵ R for all a, b, c ϵ {1,2,3,4}

Therefore, R is transitive.

Therefore, R is reflexive and transitive but not symmetric.