Example 14 - Check true or false by proving its contrapositive - Proving True - By Contrapositive

Example 14 - Chapter 14 Class 11 Mathematical Reasoning - Part 2
Example 14 - Chapter 14 Class 11 Mathematical Reasoning - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 14 Check whether the following statement is true or false by proving its contrapositive. If x, y ∈ Ζ such that xy is odd, then both x and y are odd. Let p : xy is odd. q : both x and y are odd. The given statement is of the form it p then q i.e. p ⇒ q We have to check the validity of statement by contrapositive method. i.e. x and y are not odd & prove that is false i.e. prove that xy is not odd Now consider x & y are not odd i.e. x & y are even let x = 2n for same n, m ∈ Z & t = 2m Calculate xy = 2n × 2m if n, m ∈ Z = 4mn ⇒ nm ∈ Z = 2 (2 m n) ⇒ 2n m ∈ Z This show xy is even ⇒ xy is not odd ⇒ p is false ⇒ ~ p Hence ~ q ⇒ ~ p

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.