Prove that either

a) this problem is solvable

or

b) this problem is unsolvable

Wouldn't it be possible to use the common mathematical process of Reducto ad Absurdum on this?

We start out by assuming B is true, meaning there is no solution. However, in providing the solution (b), we have provided a solution to the problem, meaning that there is a solution to a problem, which is a direct contradiction to b. So ergo, because by assuming B is true we run into a contradiction, there must be a solution. Therefore, a.

We can also try to prove a is false with Reducto ad Absurdum: Assume a is true. Since a is true, there is a solution. Since a is a solution there is a solution. This means there is no contradiction, and Reducto ad Absurdum fails.

By analyzing the problem itself, and supposing "s" represents that the problem has a solution, we get...
If: a or b then s
If: b then not s

In doing so, we say that if: b then s and not s, which is a direct contradiction, hence the answer is a.

I'm sure there's a hole in my logic somewhere, but I can't see it right now, as it's kind of late. Feel free to point it out to me, if it's there, of course.

Posted by Sniper59 on 2003-10-31 23:16:25