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

The given statement is
"For any real numbers $a$ and $b$, $a^2=b^2$ implies that $a=b$"
To show that this statement is false,
Let $a=5$ and $b=-5$
Here $a^2=25$ and $b^2=25$
$i.e.,$ $a^2=b^2$. But $5\neq -5$ $i.e.,$ $a\neq b$
$\therefore$ The given statement is false.
answered Jul 26, 2014