Question

Prove that for all integers m and n, m + n and m - n are either both odd or both even.​

Answer 1

Answer:

Case 1: Let's consider that m = 4 and n = 2

m + n = 4+2

= 6 (an even number)

m - n = 4 - 2

= 2 ( an even number)

In this case, both are even.

Case 2: Let's consider that m = 5 and n = 2

m + n = 5+2

= 7 ( odd number)

m - n = 5 - 2

= 3 (odd number)

In this case, both are odd.

Hence, it is proved that in m+n and m - n, both will be either odd or even.

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