Question

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 1

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, …}.