Q. 133.6( 7 Votes )

# 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 :

Given that, A = {1, 2, 3} and R = {1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (1, 3), (3, 2)}.

Now,

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

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

R is transitive ∵ (1,3) ∈ R and (3,2) ∈ R ⇒ (1,2) ∈ R

Thus, R is reflexive and transitive but not symmetric.

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