Question

Determine the set of all integers a such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21.

(a) {−21, −18, −11, −4, 3, 10, 16}

(b) {−21, −18, −11, −4, 3, 10, 17, 24}

(c) {−24, -19, -15, 5, 0, 6, 10}

(d) {−23, −17, −11, 0, 2, 8, 16}

I have been asked this question at a job interview.

I would like to ask this question from Relations in chapter Relations of Discrete Mathematics

Answer 1

The correct answer is (b) {−21, −18, −11, −4, 3, 10, 17, 24}

For explanation I would say: For an integer a we have x ≡ 3 (mod 7) if and only if a = 7m + 3. Thus, by calculating multiples of 7, add 3 and restrict the value of a, so that −21 ≤ x ≤ 21. The set for a = {−21, −18, −11, −4, 3, 10, 17, 24}.