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)

Last updated at April 16, 2024 by Teachoo

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.