Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}.
Show that R is reflexive but neither symmetric nor transitive.

Question

Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}. Show that R is reflexive but neither symmetric nor transitive.

Philoid · Accepted Answer

Given that, A = {1, 2, 3} and R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}.

Now,

R is reflexive ∵ (1,1),(2,2),(3,3) ∈ R

R is not symmetric ∵ (1,2),(2,3) ∈ R but (2,1),(3,2) ∉ R

R is not transitive ∵ (1,2) ∈ R and (2,3) ∈ R ⇒ (1,3) ∉ R

Thus, R is reflexive but neither symmetric nor transitive.

Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}.Show that R is reflexive but neither symmetric nor transitive.