Show that the statement “For any real ...

NCERT Class XI Mathematics - Mathematical Reasoning - Solutions

Question : 15 of 25

Marks: +1, -0

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.

Solution:

The given compound statement is of the form “if p then q”

We assume that p is true, then a, b ∈ R such that

a^2

b^2

Let us take a = –3 and b = 3

Now,

a^2

b^2

, but a ≠ b

So, when p is true, q is false.

Thus, the given compound statement is not true.

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