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.