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

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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. 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.