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Consider the congruence 45≡3(mod 7). Find the set of equivalence class representatives.(a) {…, 0, 7, 14, 28, …}(b) {…, -3, 0, 6, 21, …}(c) {…, 0, 4, 8, 16, …}(d) {…, 3, 8, 15, 21, …}I got this question by my school teacher while I was bunking the class.The above asked question is from Relations in chapter Relations of Discrete Mathematics

Answer»

The correct option is (a) {…, 0, 7, 14, 28, …}

To elaborate: Note that a set of class representatives is the subset of a set which contains exactly one element from each equivalence class. Now, for integers n, a and B, we have CONGRUENCE a≡b(MOD n), then the set of equivalence classes are{…, -2n, -n, 0, n, 2n,…}, {…, 1-2n, 1-n, 1, 1+n, 1+2n,…}. The required answer is {…, 0, 7, 14, 28, …}.



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