Ok I don't need answers just a little shove in the right direction. It's not an incredibly hard logic problem, I just want to know the best route to take to prove it. Here's the question,
If 'R' and 'S' are irrational then R^S is irrational.
I was thinking contra-positive would be best. So assume not P and prove not Q. So this means I would have 'R' and 'S' are rational and prove that R^S is rational. I know that if a number is rational then it can be represented by two integers (m/n) but I'm just not sure how to work that in to get my proof solid. Thanks in advanced.
That's a good example. So I know that we have AT LEAST one example, I'm sure more, than we can prove it is true. My problem still is what is my best bet to write a proof for this. If the question was to show and example or prove this true or false for one example that would work. My issue is I'm not sure what to do for my next step in proving that for 'the universe' of all irrational numbers this is true.
My point is I can show that there is a false one to, for example:
(Root2 ^ Root3) is going to be irrational.
You showed an example that makes two irrationals a rational number, so obviously this problem is going to be false because that right there is a contradiction. What do you think the best method of proving would be to finish this? P and not Q, then show an example???
By the way, you have your contra-positive the wrong way. If you want to prove by contra-positive, you need to prove that if q doesn't hold then neither does p; that is, in this case, you would assume that is rational, and show that either or are rational as well.