4. a) On page 552 of the textbook, they prove that the relation R on the set of integers, where m R n if, and only if, 3 | (m - n), is an equivalence relation. If you are having trouble with part a), reread pages 552 and 553 of the textbook.
b) To find the equivalence classes for r, you might like to refer to pages 566 and 567 of the textbook. It might also help to think of the equivalence classes of r as being the possible remainders when an integer is divided by 7.