

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 1.1
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 June 5, 2023 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.