Ex 1.1, 1 (i) - Chapter 1 Class 12 Relation and Functions

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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.