Question

Let A = {1, 2, 3, 4} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (1, 3), (3, 2)}. Show that R is reflexive and transitive but not symmetric.

Answer 1

It is given that

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

We know that

(1, 1), (2, 2), (3, 3), (4, 4) ∈ R is reflexive.

We know that

(1, 2) ∈ R but (2, 1) ∈ R

Hence, R is not symmetric.

The same way

(1, 2) ∈ R and (2, 3) ∈ R but (1, 3) ∈ R

Hence, R is transitive.