Relations - Definition

Chapter 2 Class 11 Relations and Functions
Concept wise

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

### Transcript

Misc 9 - Introduction Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (a, a) ∈ R, for all a ∈ N Is a = a2 Checking for different values of a 1 = 12 = 1 2 ≠ 22 3 ≠ 32 Hence, a = a2 is not always true Misc 9 Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (a, a) ∈ R, for all a ∈ N Given R = {(a, b): a, b ∈ N and a = b2} Hence we can say that (a, b) is in relation R if a, b ∈ N i.e. both a & b are natural numbers a = b2 We need to check if both these conditions are true for (a, a) 1. a, a ∈ N , i.e. a is a natural number 2. a = a2 is not always true Since both conditions are not always true. ∴ (a, a) ∉ R Hence, the given statement is False Misc 9 - Introduction Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (ii) (a, b) ∈ R, implies (b, a) ∈ R If a = b2, then b = a2 ? Let b = 2, a = b2 = 22 = 4 But 2 ≠ 42 i.e. b ≠ a2 So, If a = b2, then b = a2 is not always true Misc 9 Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (ii) (a, b) ∈ R, implies (b, a) ∈ R Given R = {(a, b): a, b ∈ N and a = b2} Given (a, b) is in relation R. So, the following conditions are true a, b ∈ N i.e. both a & b are natural numbers a = b2 We need to check if both these conditions are true for (b, a) 1. b, a ∈ N , i.e. b, a is a natural number 2. b = a2 is not always true Since, both conditions are not true. ∴ (b, a) ∉ R Hence, the given statement is False Misc 9 - Introduction Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R. If a = b2, & b = c2 , then a = c2? Let b = 4, a = b2 = 42 = 16 & 4 = c2 i.e. c = 2 But 16 ≠ 22 i.e. a ≠ c2 So, If a = b2, & b = c2 , then a = c2 is not always true Misc 9 Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true? (iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R. Given R = {(a, b): a, b ∈ N and a = b2} Given (a, b) ∈ R , i.e. (a, b) is in relation R . So, the following conditions are true a, b ∈ N i.e. both a & b are natural numbers a = b2 Given (b, c) ∈ R , i.e. (b, c) is in relation R . So, the following conditions are true b, c ∈ N i.e. both b & c are natural numbers b = c2 We need to prove both these conditions for (a, c) 1. Given a, b & b, c ∈ N, Hence a, c ∈ N 2. If a = b2, & b = c2 , then a = c2 is not always true Since both the conditions are not true Hence, (a, c) ∉ R So, the given statement is False

#### 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.