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

djeljenike 2021-02-05 Answered
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.
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## Expert Answer

Nicole Conner
Answered 2021-02-06 Author has 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.
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