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1. For each statement that is true, give a proof and for each false statement, give...

1. For each statement that is true, give a proof and for each false statement, give a counterexample

    (a) For all natural numbers n, n2 +n + 17 is prime.

    (b) p Þ q and ~ p Þ ~ q are NOT logically equivalent.

    (c) For every real number x ³ 1, x2£ x3.

    (d) No rational number x satisfies x^4+ 1/x -(x+1)^(1/2)=0.

    (e) There do not exist irrational numbers x and y such that logx y is rational

    (f) n^2+3n+7 is odd for all integers n.    

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