q) is true, we assume that p is
true and use that to show that q must also be true.3. To prove that an if--then statement (p q) is true, we assume that p is
true and use that to show that q must also be true.
Proof Suppose that a - b = rm and b - c = sm for some integers r and s.
| Add the two equations to get: a - b + b - c | = | rm + sm |
| a - c | = | rm + sm |
| a - c | = | (r + s)m |
| a - c | = | tm, where t = r + s |
Since r and s are integers, r + s is an integer. Therefore a - c = tm for some integer t.