Question 2 - Proving Statements true or false - Mathematical Reasoning

Last updated at April 16, 2024 by

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

Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.