(1) Mimic the proof given in the sample solutions for the proposition if a > 0 a

Question

(1) Mimic the proof given in the sample solutions for the proposition if a > 0 and
b > 0, then ab > 0 to prove:
(a) If a < 0 and b < 0, then ab > 0.
(b) If a < 0 and b > 0, then ab < 0.

Example:
Prove that if a > 0 and b > 0, then ab > 0.
Solution: Suppose the integers a and b are both greater than 0.
Since a > 0, multiplying both sides of 0 < b by a will give a0 < ab according to one of the
rules of inequalities given in the lesson. A theorem proved in this lesson tells us a0 = 0. So
a0 < ab is the same as 0 < ab, and that is what we needed to show.

Explanation / Answer

(a) If a < 0 and b < 0, then ab > 0. if a0 (b) If a < 0 and b > 0, then ab

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