prove or disprove each of the following statements. (a) for all integers a, b, and c, if a | b and a | c, then a | (b c) (b) for all integers a, b, and c, if a | b or a | c, then a | (b c) (c) for all integers a, b, and c, if a | b and a | c, then a | bc (d) for all integers a, b, and c, if a | b or a | c, then a | bc (e) for all integers a, b, and c, if a | b and a | c, then a2 | bc (f) for all integers a, b, and c, if a | bc, then a | b or a | c.