djeljenike

2021-02-05

Using "Proof by Contraposition",sho that: if n is any odd integer and m is any even integer, then, $3{m}^{3}+2{m}^{2}$ is odd.

Nicole Conner

Skilled2021-02-06Added 97 answers

Let n be odd integer and m be even integer claim: $3{m}^{3}+2{m}^{2}$ is odd.

We will prove this by contradiction.

On contrary suppose$3{m}^{3}=2{m}^{2}$ is not odd.

i.e.$3{m}^{3}=2{m}^{2}$ is even

$\therefore 3{m}^{3}$ is even

$\therefore {m}^{3}$ is even

$\therefore m$ is even

which is contradiction

$\therefore$ our supposition is wrong

$\therefore 3{n}^{3}+2{m}^{2}$ is odd.

We will prove this by contradiction.

On contrary suppose

i.e.

which is contradiction

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