Suppose that R is a relation X  that is symmetric and transitive but not reflexive. Suppos...

Suppose that R is a relation X  that is symmetric and transitive but not reflexive. Suppose also that |X| ≥ 2. Define the relation  on X by

Which of the following must be true? For each false statement,  provide a counterexample.

(a)  is reflexive.

(b)  is symmetric.

(c)  is not antisymmetric.

(d)  is transitive.