Prove or disprove: a) For all integers a, b, c, if a | b and b|c then a|c. b) For all integers a, b, c, d, if a | b

and c | d, then (ac)| (b+d). c) For all integers a, b, c, if a | (b+c), then a | b and a | c. d) For all integers a, b, c, if a | bc, then a | b or a | c. e) For all integers a, b, c, if a | c and b | c, then ab |c².