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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 |
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Answer» Option : (a). {1, 5, 9} \(\because |1-1|=0\) which is a multiple of 4 Therefore, \((1, 1) \in R\) and \(|1-5|=4\) which is a multiple of 4 Therefore, \((1, 5) \in R\) Also \(|1-9|=8\) which is a multiple of 4 Therefore, \((1, 9) \in R\) Since, \((1, 1), (1, 5), (1, 9) \in R\) Therefore, the equivalence class of 1 is [1] = {1, 5, 9} |
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