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.

Solution:

The given statement can be written as follows. "If a and b are real numbers such that a² = b², then a = b".

The given statement has to be proved false. For that we need two real numbers a and b such that a² = b² where a ≠ b .

Let a = 1 and b = - 1

Then, a² = 1² = 1 and b² = (- 1)² = 1

Here, a² = b²

However, a ≠ b

Thus, it can be concluded that the given statement is false

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.5 Question 2

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

Summary:

It is proved that the given statement is false