For each of the following statements about relations on a set A, where |A| = n, determine whether the statement is true or false. If it is false, give a counterexample.
(a) If R is a relation on A and |R| ≥ n, then R is reflexive.
(b) If R1, R2 are relations on A and R2 ⊇ R1, then R1 reflexive (symmetric, antisymmetric, transitive) ⇒ R2 reflexive (symmetric, antisymmetric, transitive).
(c) If R1, R2 are relations on A and R2 ⊇ R1, then R2 reflexive (symmetric, antisymmetric, transitive) ⇒ R1 reflexive (symmetric, antisymmetric, transitive).
(d) If R is an equivalence relation on A, then n ≤ |R| ≤ n2.