Let A = {1, 2, 3, 4, 5} × {1, 2, 3, 4, 5}, and define R on A by (x1, y1) R (x2, y2) if x1 + y1 = x2 + y2.
(a) Verify that R is an equivalence relation on A.
(b) Determine the equivalence classes [(1, 3)], [(2, 4)], and [(1, 1)].
(c) Determine the partition of A induced by R.