Prove that if m and n are integers and nm is even, then m is even or n is even. What is the best approach here, direct proof, proof by contraposition, or proof by contradiction - why?

Question

Mathematics

Lilyana Mendoza

24 December, 07:50

Prove that if m and n are integers and nm is even, then m is even or n is even. What is the best approach here, direct proof, proof by contraposition, or proof by contradiction - why?

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Answers (1)

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Mireya Duffy · Answer 1

Proof by contraposition

Step-by-step explanation:

If m and n both are odd, then mn is also odd.

m and n are integers which is not divisible by 2,

Therefore,

m*n is also not divisible by 2.

Which means mn is odd.