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Last updated at Aug. 11, 2021 by Teachoo

Transcript

Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} R = {(x, y): y = x + 5 and x < 4} Here x & y are natural numbers, & x < 4 So, we take value of x as 1 , 2, 3 R = {(1, 6), (2, 7), (3, 8)} Check Reflexive If the relation is reflexive, then (a, a) R for every a N Since (1, 1) R R is not reflexive Check symmetric To check whether symmetric or not, If (a, b) R, then (b, a) R Here (1, 6) R , but (6, 1) R R is not symmetric Check transitive To check whether transitive or not, If (a, b) R & (b, c) R , then (a, c) R There is no pair in R such that (a, b) R and (b, c) R , then (a, c) R. R is not transitive Hence, R is neither reflexive, nor symmetric, nor transitive.

Ex 1.1

Ex 1.1, 1 (i)

Ex 1.1, 1 (ii) You are here

Ex 1.1, 1 (iii) Important

Ex 1.1, 1 (iv)

Ex 1.1, 1 (v)

Ex 1.1, 2

Ex 1.1, 3

Ex 1.1, 4

Ex 1.1, 5 Important

Ex 1.1, 6

Ex 1.1, 7

Ex 1.1, 8 Important

Ex 1.1, 9 (i) Important

Ex 1.1, 9 (ii)

Ex 1.1, 10 (i)

Ex 1.1, 10 (ii)

Ex 1.1, 10 (iii) Important

Ex 1.1, 10 (iv)

Ex 1.1, 10 (v)

Ex 1.1, 11

Ex 1.1, 12 Important

Ex 1.1, 13

Ex 1.1, 14

Ex 1.1, 15 (MCQ) Important

Ex 1.1, 16 (MCQ)

Chapter 1 Class 12 Relation and Functions (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.