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Mathematical Reasoning — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsMathematical Reasoning2 Marks
Question
Using contrapositive method prove that if $n\ 2$ is an even integer, then $n$ is also an even integers.
✓

Answer

Let $p: n^2$ is an even integer.
$q: n$ is also an even integer.
Let $\sim p$ is true i.e., $n$ is not an even integer.
$\Rightarrow n^2$ is not an even integer. $[$Since square of an odd integer is odd$]$
$⇒ \sim p$ is true.
Therefore, $\sim q $ is true which provides that $\sim p$ is true.
Hence proved.

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