Question

For a, b ∈ R define a = b to mean that |x| = |y|. If [x] is an equivalence relation in R. Find the equivalence relation for [17].

(a) {,…,-11, -7, 0, 7, 11,…}

(b) {2, 4, 9, 11, 15,…}

(c) {-17, 17}

(d) {5, 25, 125,…}

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Question is from Relations in section Relations of Discrete Mathematics

Answer 1

Right answer is (c) {-17, 17}

Explanation: We can find that [17] = {a ∈ R|a = 17} = {a ∈ R||a| = |17|} = {-17, 17} and [−17] = {a ∈ R|a = −17} = {a ∈ R||a| = |−17|}= {−17, 17}. Hence, the required equivalence relation is {-17, 17}.