Hint for Section 3.6 Question 3 (by contraposition)

3.. We are asked to prove, using the method of contraposition, the statement: "rQ with r non-zero, if (s is irrational), then (r·s is irrational).

The contrapositive of the above statement is:  "rQ with r non-zero, if (r·s is rational), then (s is rational).

Now prove the contrapositive by a direct proof.

Proof Suppose that r is a non-zero rational number and the product r·s is also rational.  Thus,  there exist integers a, b, c and d such that  r = a / b and  r·s = c / d,
where a, b, d 0. 

Now try to write s in terms of a, b, c and d, and use this to prove that s is rational.

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