Question: Problem 4. (6 x 2 points) The modulo operation returns the remainder after a division. For example, 7 mod 1 = 3 because 7 =1

Problem 4. (6 x 2 points) The modulo operation returns the remainder after a division. For example, 7 mod 1 = 3 because 7 =1 . 4+3. Let a, be Z. In particular, we say that a is congruent to b modulo m if Ik c Z such that a - b = kin and we use the notation a=b (mod m) (a) Prove that the congruence relation is an equivalence relation. (b) The set {k c Z : a = k ( mod m)) is called the congruence class of a modulo m. How can we use this definition to construct a collection of sets {5:}, such that Sins, = ( whenever i / y and UPd' S, - Z? [ Hint: Consider {0, 1, ..., m - 1). It is called the least residue system modulo m]

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