q) is true, we assume that p is true and use that to show
that q must also be true.3. This question can be rewritten as an if--then statement. If
r is a rational number, then there exists another rational number s such that r + s = 0 =
s + r. 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 r is
a rational number. Hence r = a/b for some integers a and b, where b 
0.
Let s = -a/b. Then s is a rational number, since -a
and b are both integers and b 0. Furthermore,
| a/b + (-a/b) | = | (a + (-a))/b |
| = | 0/b | |
| = | 0. | |
| By the same reasoning (-a/b) + a/b | = | 0. |
Therefore for any rational number r = a/b, an additive inverse exists, namely the rational number -a/b.