Show that the statement “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example.

Asked by Pragya Singh | 11 months ago |  88

1 Answer

Solution :-

The given statement can be written in the form of ‘if then’ is given below

If a and b are real numbers such that a2 = b2, then a = b

Let p: a and b are real numbers such that a2 = b2

q: a = b

The given statement has to be proved false. 

To show this, two real numbers, a and b, with a2 = bare required such that a ≠ b

Let us consider a = 1 and b = – 1

a2 = (1)= 1

and

b2 = (-1)= 1

Hence, a2 = b2

However, a ≠ b

Therefore, it can be concluded that the given statement is false.

Answered by Sudhanshu | 11 months ago

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