Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

(a) {1, 5, 9}         (b) {0, 1, 2, 5}

(c) ϕ                    (d) A

 

This question is inspired from Ex 1.1, 9 (i) - Chapter 1 Class 12 - Relation and Functions

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Question 11 Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is: (a) {1, 5, 9} (b) {0, 1, 2, 5} (c) 𝜙 (d) A Given R = {(a, b) : |a – b| is a multiple of 4} & A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Here a = 1, We need to find values of b such that (a, b) ∈ R The set of elements related to 1 are {1, 5, 9} So, the correct answer is (a)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.