1. For each of the following statements determine whether the statement is true or false.If the statement is true provide a proof, if it is false give a suitable counterexample. (a) Let m and n be integers. If m is even and n is odd, then mn is even. (b) If x and y are irrational numbers, then xy is irrational. (c) Let n be an integer, then n² is odd ⇒ n is odd. (d) For all integers m, m² + m + 17 is prime.

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