set 2 q 7 - looking for a detailed worked solution

17. Prove for a, b, c, de Z, k, m E Z+ that a) if a c and b d then ab ed, b) if ab bd and b / 0, then a | d. c) if a | b and b c then a c, d) if a = c (mod m) and b = d (mod m) then a - b= c -d (mod m), e) if k | m and a = b (mod m) then a = b (mod k), f) if d = ged(a, b) then god ( 92) =1 *g) if a = b (mod m) then god(a, m) = god(b, m)