Ex 14.5, 2 - Show that statement 'For any real numbers a and b - Proving not true/false (by giving counter examples)

  1. Chapter 14 Class 11 Mathematical Reasoning
  2. Serial order wise
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Ex 14.5, 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. Let a = – 1 & b = 1 Calculating a2 & a2 a2 = ( – 1)2 = 1 b2 = (1)2 = 1 Since a2 = b2 = 1 ( – 1)2 = (1)2 But a ≠ b ⇒ – 1 ≠ 1 Hence the given statement is not true.

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