Consider the statement :

Question:

Consider the statement :

$q$ : For any real numbers $a$ and $b, a^{2}=b^{2} \Rightarrow a=b$ By giving a counter-example, prove that $q$ is false.

 

Solution:

Let us take the numbers a= +5 and b= -5.

$2=(+5)^{2}=25$

$b^{2}=(-5)^{2}=25$

$\therefore a^{2}=b^{2}$

But, $+5 \neq-5$, thus $a \neq b$.

$\therefore \mathrm{q}$ is false.

 

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