For each of the following statements about relations on a set A, where |A| = n,

Question

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 R_1,R_2are relations on A and R_2? R_1, then R_1reflexive (symmetric, antisymmetric, transitive) ? R_2 reflexive (symmetric, antisymmetric, transitive). C) If R_1,R_2 are relations on A and R_2?R_(1 ), then R_2 reflexive (symmetric, antisymmetric, transitive) ? R_1reflexive (symmetric, antisymmetric, transitive). D) If R is an equivalence relation on A,then n?|R|?n^2.

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