What is the correct answer to the following questions?

Question

Let A = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows:

For all x, y  A, x R y ⇔ 3|(x − y).

It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R.

[0]=

[1]=

[2]=

[3]=

How many distinct equivalence classes does R have?

List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Answer 1

[0] contains all elements of A that are multiples of 3.

[1] contains all elements of A that leave a remainder of 1 when divided by 3.

[2] contains all elements of A that leave a remainder of 2 when divided by 3.

[3]=[0].

So there are 3 distinct equivalence classes.