Misc  6 - Chapter 14 Class 11 Mathematical Reasoning - Part 3

Misc  6 - Chapter 14 Class 11 Mathematical Reasoning - Part 4

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Transcript

Misc, 6 Check the validity of the statements given below by the method given against it. (ii) q: If n is a real number with n > 3, then n2 > 9 (by contradiction method). q : if n is real number with n > 3 then n 3 > 9 Let the component statement is given in the form if p then q By contradiction method By assuming if p then q & we get a contradiction that our assumption is Wrong It p then q let n > 3 & n2 9 Put n = + 1 + a. Squaring both side. (n)2 = (3 + a)2 (n)2 = (3)2 + (a)2 + 2 3 a (n)2 = 9 + a2 + 6a (n)2 =9 + a (6 + 9) (n)2 > 9 hence n2 > 9 We get a contradictive because we assume n2 9 Hence the given statement is live .

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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.