Ex 1.1, 1 (i) - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
Ex 1.1
Ex 1.1, 1 (i)
You are here
Ex 1.1, 1 (ii)
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
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)
Transcript
Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(x, y): 3x − y = 0} R = {(x, y): 3x − y = 0} So, 3x – y = 0 3x = y y = 3x where x, y ∈ A ∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ A i.e. {1, 2, 3…13, 14} Since (1, 1) ∉ R ,(2, 2) ∉ R , (3, 3) ∉ R , …. (14, 14) ∉ R ∴ R is not reflexive Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R Here (1, 3) ∈ R , but (3, 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 Here, (1, 3) ∈ R and (3, 9) ∈ R but (1, 9) ∉ R. ∴ R is not transitive Hence, R is neither reflexive, nor symmetric, nor transitive.
