Consider the statement: For all integers n, if n3 is even then n is even. a. Explicitly write out what you are supposing and what you are trying to prove, if you are proving the statement by proving the contrapositive. Suppose Need to show b. Prove the statement by the method of the contrapositive

It is proved that if is even the n is even.

Step-by-step explanation:

Given n is any integer.

To show is even then n is even.

Proving by contrapositive suppose is odd. Then we need to show n is odd.

Then, letting k is a ny integer,

Now since (2k+1) is odd therefore n is odd.

Conversly let n is odd, then,

since 2k+1 is odd so is odd.

This proves, if n is even then is even.

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step-by-step explanation: