Check sibling questions

Ex 14.5, 3 - Show true by method of contrapositive - Proving True - By Contrapositive

Ex 14.5,  3 - Chapter 14 Class 11 Mathematical Reasoning - Part 2

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 14.5, 3 Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2 is even, then x is also even. p: If x is an integer and x2 is even, then x is also even. Let p: If x is an integer and x2 is even. q: x is even. The given statement is if p then q Method of contrapositive let q is not true & prove p is also not true. q is not true i.e. x is not even i.e. x is odd i.e. x = 2n + 1 Squaring both side (x)2 = (2n + 1 )2 x2 = (2n)2 + (1)2 + 2 2n 1 x2 = 4n2 + 1 + 4n x2 = 4n2 + 4n + 1 x2 = 4 (n2 + n ) + 1 x2 = 4 (n2 + n ) + 1 x2 is odd p is also not true a Hence the given statement is true

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.