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You must show all work performed for the questions below. You will not receive credit for...

You must show all work performed for the questions below. You will not receive credit for an answer without detailed work.

5. Prove or disprove each of the following claims:

(a) For all positive integers, n is even if and only if 3n^2 + 8 is even.

(b) If a and b are rational numbers, then a^2 + b^2 ≥ 2ab.

(c) If n is an even integer, then n + 1 is odd.

(d) Every odd number is the difference of two perfect squares.

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