Recall that for x, y = Z, x=y (mod 5) provided that x - y = 5t for some 8. te Z. Describe the equivalence class of 0 under this equivalence relation.

14. a. Let R be the relation of congruence modulo 3. Which of the following equivalence classes are equal? [7], [-4], [-6], [17], [4], [27], [19] b. Let R be the relation of congruence modulo 7. Which of the following equivalence classes are equal? [35], [3], [-7], [12], [0], [-2], [17]

Define - on Z as follows. Suppose that a ~ b if a² = b² (mod 6). Prove that - is an equivalence relation.

) 7. Let A = {1,2,3,4}×{1,2,3,4}. Define an equivalence relation - by (x1,x2) ~ (X3,x4) iff x1x2 = xx4. List the elements of the equivalence class [(2,2)].