Check sibling questions

Examples

Example 1 (i) Deleted for CBSE Board 2022 Exams

Example 1 (ii) Important Deleted for CBSE Board 2022 Exams

Example 1 (iii) Deleted for CBSE Board 2022 Exams

Example 1 (iv) Important Deleted for CBSE Board 2022 Exams

Example 1 (v) Deleted for CBSE Board 2022 Exams

Example 1 (vi) Deleted for CBSE Board 2022 Exams

Example 2 (i) Important Deleted for CBSE Board 2022 Exams

Example 2 (ii) Deleted for CBSE Board 2022 Exams

Example 3 (i) Deleted for CBSE Board 2022 Exams

Example 3 (ii) Important Deleted for CBSE Board 2022 Exams

Example 3 (iii) Deleted for CBSE Board 2022 Exams

Example 3 (iv) Deleted for CBSE Board 2022 Exams

Example 4 (i) Deleted for CBSE Board 2022 Exams

Example 4 (ii) Deleted for CBSE Board 2022 Exams

Example 4 (iii) Important Deleted for CBSE Board 2022 Exams

Example 4 (iv) Important Deleted for CBSE Board 2022 Exams

Example 5 (i) Deleted for CBSE Board 2022 Exams

Example 5 (ii) Important Deleted for CBSE Board 2022 Exams

Example 5 (iii) Deleted for CBSE Board 2022 Exams

Example 5 (iv) Important Deleted for CBSE Board 2022 Exams

Example 5 (v) Deleted for CBSE Board 2022 Exams

Example 5 (vi) Important Deleted for CBSE Board 2022 Exams

Example 6 (i) Deleted for CBSE Board 2022 Exams

Example 6 (ii) Important Deleted for CBSE Board 2022 Exams

Example 6 (iii) Deleted for CBSE Board 2022 Exams

Example 7 (i) Deleted for CBSE Board 2022 Exams

Example 7 (ii) Important Deleted for CBSE Board 2022 Exams

Example 7 (iii) Deleted for CBSE Board 2022 Exams

Example 7 (iv) Important Deleted for CBSE Board 2022 Exams

Example 8 (i) Deleted for CBSE Board 2022 Exams

Example 8 (ii) Important Deleted for CBSE Board 2022 Exams

Example 8 (iii) Deleted for CBSE Board 2022 Exams

Example 9 Deleted for CBSE Board 2022 Exams

Example 10 Important Deleted for CBSE Board 2022 Exams

Example 11 (i) Deleted for CBSE Board 2022 Exams

Example 11 (ii) Important Deleted for CBSE Board 2022 Exams

Example 12 (i) Deleted for CBSE Board 2022 Exams

Example 12 (ii) Deleted for CBSE Board 2022 Exams

Example 13 Important Deleted for CBSE Board 2022 Exams You are here

Example 14 Important Deleted for CBSE Board 2022 Exams

Example 15 Important Deleted for CBSE Board 2022 Exams

Example 16 Deleted for CBSE Board 2022 Exams

Example 17 Deleted for CBSE Board 2022 Exams

Example 18 (i) Deleted for CBSE Board 2022 Exams

Example 18 (ii) Important Deleted for CBSE Board 2022 Exams

Example 18 (iii) Deleted for CBSE Board 2022 Exams

Example 18 (iv) Deleted for CBSE Board 2022 Exams

Example 19 Important Deleted for CBSE Board 2022 Exams

Example 20 Important Deleted for CBSE Board 2022 Exams

Chapter 14 Class 11 Mathematical Reasoning (Deleted)
Serial order wise

Example 13 - Check whether true or not. If x and y are odd - Proving True - If and only if

Example 13 - Chapter 14 Class 11 Mathematical Reasoning - Part 2
Example 13 - Chapter 14 Class 11 Mathematical Reasoning - Part 3
Example 13 - Chapter 14 Class 11 Mathematical Reasoning - Part 4
Example 13 - Chapter 14 Class 11 Mathematical Reasoning - Part 5

Are ads bothering you?


Transcript

Example 13 Check whether the following statement is true or not. If x, y ∈ Z are such that x and y are odd, then xy is odd. Statement : If x & y ∈ Z are such that x & y are odd, then xy is odd Let p : x , y ∈ Z such . that x and y are odd q : xy is odd That given statement is of the form if p ⇒ q We check the validity of the given statement Statement : If x & y ∈ Z are such that x & y are odd, then xy is odd Method 1 :- Direct Method By assuming that p is true, prove that q must be true. i.e. Assuming x & y are odd , prove that xy is odd Since x & y are odd Let x = 2m + 1 When m, n ∈ Z & y = 2n + 1 Calculating xy = (2m + 1 ) (2n + 1) = 2m (2n + 1 ) + 1 (2n + 1 ) = (2m) (2n) + 2m + 2n + 1 = 4mn + 2m + 2n + 1 = 2 (mn + m + n) + 1 This shows xy is odd Hence q is true. Therefore the given statement is true Method 2 :- Contrapositive Method Statement : If x & y ∈ Z are such that x & y are odd, then xy is odd By assuming that q is false, prove that p must be false. Let xy be not odd , prove that x and y are not odd Since xy is not odd ⇒ xy is even. ⇒ This is possible only if either x or y is even Let us take an example

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.