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If $a$ and $b$ are real numbers such that $a_{2}=b_{2}$ then $a=b$

Let $p:a$ and $b$ are real numbers such that $a_{2}=b_{2}$

$q:a=b$

The given statement has to be proved false.

For this purpose it has to be proved that if $p$ then $∼q$

To show this two real numbers $a$ and $b$ with $a_{2}=b_{2}$ are required such that

$a=b$

Let $a=1$ and $b=−1$

$a_{2}=(1)_{2}=1$ and $b_{2}=(−1)_{2}=1$

$∴a_{2}=b_{2}$

However $a=b$

Thus it can be concluded that the given statement is false

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