Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Question

State True or False for the statement:

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Answer 1

False

Given that, R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}

Now,

R is not reflexive ∵ (1,1),(2,2) ∉ R.

R is symmetric ∵ (3,1) ∈ R ⇒ (1,3) ∈ R

R is not transitive ∵ (1,3) ∈ R and (3,1) ∈ R but (1,1) ∉ R.