Every relation which is symmetric and transitive is also reflexive.

Question

State True or False for the statement:

Every relation which is symmetric and transitive is also reflexive.

Answer 1

False

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

Now,

R is not reflexive ∵ (2,2) ∉ R.

R is symmetric ∵ (1,2) ∈ R ⇒ (2,1) ∈ R

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

Thus, It is not true that every relation which is symmetric and transitive is also reflexive.