Last updated at Aug. 11, 2021 by

Transcript

Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (iv) Relation R in the set Z of all integers defined as R = {(x, y): x y is as integer} R = {(x, y): x y is as integer} Check Reflexive Since, x x = 0 & 0 is an integer x x is an integer (x, x) R R is reflexive Check symmetric If x y is an integer, then (x y) is also an integer, y x is an integer So, If x y is an integer, then y x is an integer i.e. If (x, y) R, then (y, x) R R is symmetric Check transitive If x y is an integer & y z is an integer then, sum of integers is also an integer (x y) + (y z) is an integer. x z is an integer. So, If x y is an integer & y z is an integer then, x z is an integer. If (x, y) R & (y, z) R , then (x, z) R R is transitive Hence, R is reflexive, symmetric, and transitive.

Ex 1.1

Ex 1.1, 1 (i)

Ex 1.1, 1 (ii)

Ex 1.1, 1 (iii) Important

Ex 1.1, 1 (iv) You are here

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

Ex 1.1, 9 (i)

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.