# 2.    Show that the statement “For any real numbers a and b, $a^2 = b^2$ implies that $a = b$” is not true by giving a counter-example.

Given,

For any real numbers a and b, $a^2 = b^2$ implies that $a = b$.

Let a = 1 & b = -1

Now,

$\dpi{100} a^2 = (1)^2$= 1

$\dpi{100} b^2 = (-1)^2$ = 1

$\implies a^2 =1= b^2$

But a $\dpi{80} \neq$ b

Hence $a^2 = b^2$ does not imply that $a = b$.

Hence the given statement is not true.

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