Math 301
Quiz 8
Show all work in a neat and organized fashion. Clearly indicate your answers.
10 points possible.
1. (4 pts.) A student is asked to prove that the difference
of any rational number and any irrational number is irrational.
The student begins: ``Suppose, to the contrary, that the
difference of any rational number and any irrational number
is rational. We must deduce a contradiction.'' Fix the
beginning (but don't finish the proof).
2. (6 pts.) Use the principle of mathematical induction
to prove that for all positive integers n,
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