Hello, Don!

Let R be the relation congruence modulo 4.

Which of the following equivalence classes are equal?

[7], [-3], [5],[-27], [32], [-14], [243], [9]

I first began the problem by setting up four classes: 0, 1, 2, and 3. . . . . Good!

I then divided each number, for example 7 divided by 4 which yielded a remainder 3.

So, 7 would be in class 3. . . . . Right!

I know how to do the positive numbers, but how would I go about doing the negative?

Use the same procedure.

If you get a negative remainder, use the modulo to "make it positive".

For example: .

. . And we know that: .

. . Therefore: .