Question: QUESTION 12. [4 POINTS] (a) Let R be a relation on the set Z x Z defined by the following rule: R = {((a, b),

QUESTION 12. [4 POINTS] (a) Let R be a relation on the set Z x Z defined by the following rule: R = {((a, b), (c, d)) c Z x Z | 3a + c= 3b + d} Is R reflexive ? Answer with 'YES' or 'NO'. If your answer is 'YES', give a detailed proof. If your answer is 'NO', provide an a counterexample and explain. (b) Let S be a relation on the set Z, defined by the following rule: R = {(a, b) c Z x Z | 5a + 3b is even } Is S transitive? If so, give a detailed proof. If not, provide an appropriate count and explain

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