9. For each of the following statements about relations on a set A, where |A| 

Question

9. 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  is a relation on A and || ? n, then  is reflexive. b) If 1, 2 are relations on A and 2 ? 1, then 1 reflexive (symmetric, antisymmetric, transitive) ?2 reflexive (symmetric, antisymmetric, transitive). c) If 1, 2 are relations on A and 2 ? 1, then 2 reflexive (symmetric, antisymmetric, transitive) ?1 reflexive (symmetric, antisymmetric, transitive). d) Ifis an equivalence relation on A, then n ? || ? n2.

Explanation / Answer

A.true B.false. C.false D.true

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