Hi Iam am just starting to understand proofs and i want to make sure that I am u

Question

Hi Iam am just starting to understand proofs and i want to make sure that I am understanding all the concepts. tips on proofs are appreciated!


1) Prove that if n is an integer, then (n^3) - n is even.
2) Prove that if n is an integer, then 3n + 1 and 5n + 2 are opposite parity.
3) Let m and n be two integers. Prove that if n and n are opposite parity, then 2m + n and 3m - 4n are
opposite parity.
4) Let S = {0, 1, 3, 4}. Prove that if x is an element of S, then (x^2) - 4x +3 = 0 or (x^2) - 4x + 3 = 3.

Explanation / Answer

1)n^3 will always be even when n is even. n^3 will only be odd when n is odd. An even number minus an even number = an even number. An odd number minus an odd number = an even number. 2) since the product is always even they are opposite parity

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