Let R be the relation congruence modulo 4.
Which of the following equivalence classes are equal?
, [-3], ,[-27], , [-14], , 
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: .