Ex 1.1, 10 (iv) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 1.1, 10 Given an example of a relation. Which is (iv) Reflexive and transitive but not symmetric. Let A = {1, 2, 3}. Let relation R on set A be Let R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1,2,3} Since (1, 1), (2, 2), (3, 3) ∈ R ∴ R is reflexive Check Symmetric Since (1, 2) ∈ R , but (2, 1) ∉ R If (a, b) ∈ R, then (b, a) ∉ R ∴ R is not symmetric. Check transitive Since (1, 2) ∈ R , (2, 3) ∈ R & (1, 3) ∈ R So, If (a, b) ∈ R , (b, c) ∈ R , then (a, c) ∈ R ∴ R is transitive. Hence, relation R is reflexive and transitive but not symmetric.
Ex 1.1
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) You are here
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)
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