Determine if each of the following statements is true or false. If a statement is true, then write a formal proof of that statement, and if it is false, then provide a counterexample that shows it is false. a. For all integers a, b, and c with a ≠ 0, if a | b, then a | (bc).
b. For all integers a and b with a ≠ 0, if 6 | (ab), then 6 | a or 6 | b.
c. For all integers a, b, and c with a ≠ 0, if a divides (b - 1) and a divides (c - 1), then a divides (bc - 1).
d. For each integer n, if 7 divides (n^2 - 4), then 7 divides (n - 2).