Question: (a) Prove that if n is an odd integer, then 3n 2 + 1 is an integer multiple of 4. (b) Give a proof by

(a) Prove that if n is an odd integer, then 3n 2 + 1 is an integer multiple of 4.

(b) Give a proof by contraposition of the following theorem: If m and n are integers and 3m + n is even, then m + n is even. (c) Give a proof by contradiction of the following theorem: The product of a nonzero rational and an irrational number is irrational.

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