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  • 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.

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.

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best_answer

Given,

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

Let a = 1 & b = -1

Now,

a^2 = (1)^2= 1

b^2 = (-1)^2 = 1

\implies a^2 =1= b^2

But a \neq b

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

Hence the given statement is not true.

Posted by

HARSH KANKARIA

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