Questtion 1 -Let A = {1, 2, 3, 4, 5, 6} and let R={(5,3), (6,3), (1,2), (2,1), (5,5), (1,4), (2,2), (3,3), (4,1), (2,4), (6,6), (6,5), (4,2), (3,5), (1,1), (3,6), (4,4), (5,6)}. Draw the digraph (arrow diagram) of R. Is R an equivalence relation? If it is, then find the partition that goes with it.

Question 2-Let a, b, c, d, m, n be integers. (a) Prove that if a b (mod m) and c d (mod n), then ac + bd ad + bc (mod mn). (b) Prove that if a b (mod n) and m|n, then a b (mod m).