1. prove the following:
if n2 is not divisible by 3, then n is not divisible by 3.
(a) what kind of proof will you use to show this fact (proof by contrapositive? proof by contradiction? direct proof? proof by cases? etc.)
(b) show the fact.
2. identify the problem in the following proof that if n2 is rational, then n is rational (note: that fact is not true. consider \sqrt{2} ).
suppose n2 is rational. then n2 = \frac{a^{2}}{b^{2}} , so n = \frac{a}{b} . thus n is rational.