Subject: More Theorems to Try to Prove
From: "William J. Rapaport"
Date: Mon, 12 Oct 2009 19:29:50 -0400 (EDT)
Here are some more theorems to practice your proving strategies on.
I will post the answers on Friday, to help you study for the midterm.
For each of these, first try to represent the proposition in FOL.
Then try to prove it.
1. If n+1 is an odd integer, then n+3 is an odd integer.
2. If x and y are odd integers, then 3x+2y is an odd integer.
3. n is odd iff 5n+3 is even
4. For all real numbers x and y, max(x,y) = (x + y + |x-y|)/2
5. The square of every odd integer is of the form 8k+1,
where k is an integer.
6. Any 3 reals such that each is less than the sum of the other two
are all positive.