State True or False for the statements
Every relation which is symmetric and transitive is also reflexive.

Question

State True or False for the statements Every relation which is symmetric and transitive is also reflexive.

Philoid · Accepted Answer

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.

State True or False for the statementsEvery relation which is symmetric and transitive is also reflexive.