Question: Prove that for any integer x, 5x 2 is even if and only if 3x + 1 is odd. Comments: The phrase if and only

Prove that for any integer x, 5x 2 is even if and only if 3x + 1 is odd. Comments: The phrase if and only if just means that you have to show both directions, i.e., prove the implication if 5x2 is even, then 3x+1 is odd, as well as the implicationif 3x + 1 is odd, then 5x 2 is even.

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