r · r' = 1 = r' · 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.4. This question can be rewritten as an if--then statement. If
r is a non-zero rational number, then there exists another rational number r', such that
r · r' = 1 = r' · 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 non-zero rational number; hence r = a/b for some integers a and b, where a 
0 and
b 0.
We are trying to conclude that there exists a rational number r' such that r · r' = 1 = r' · r. To accomplish this you need to find r' (in terms of a and b).