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5. Prove or disprove the following statements: (a) Let R be a relation on the set...

5. Prove or disprove the following statements:

(a) Let R be a relation on the set Z of integers such that xRy if and only if xy ≥ 1. Then, R is irreflexive.

(b) Let R be a relation on the set Z of integers such that xRy if and only if x = y + 1 or x = y − 1. Then, R is irreflexive.

(c) Let R and S be reflexive relations on a set A. Then, R − S is irreflexive.

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