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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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
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