NCERT Class XI Mathematics - Mathematical Reasoning - Solutions

Question : 15

Total: 25

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 compound statement is of the form “if p then q”
We assume that p is true, then a, b ∈ R such that a2 = b2
Let us take a = –3 and b = 3
Now, a2 = b2, but a ≠ b
So, when p is true, q is false.
Thus, the given compound statement is not true.

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