A Question about Logical Consistency in Formal Logic

[KiwiKid]

First of all, I wasn't quite sure in which (sub)forum to post this, so if it doesn't quite fit, feel free to move it. I'm having a very hard time solving this one (or even seeing if it's logically consistent), and any help would be very much appreciated.

Homework Statement

Give a formal proof for the following conclusion:
$(\neg P \wedge \neg\neg\neg P) \vee P$

Homework Equations

There aren't any premises, so we're supposed to show that the conclusion is logically consistent.

The Attempt at a Solution

Beside the fact that I'm quite new to formal logic and don't really know how to start with this (having tried multiple things), there's something more important that's bothering me: I don't think this conclusion IS logically consistent.

You see, the logical OR is an inclusive-OR, which means that in the above case, you can have BOTH $\neg P$ and $P$. But that makes no sense. Is that correct, or am I missing something? Can you still give a 'formal proof' for any such thing?

 

[dkotschessaa]

First of all, I wasn't quite sure in which (sub)forum to post this, so if it doesn't quite fit, feel free to move it. I'm having a very hard time solving this one (or even seeing if it's logically consistent), and any help would be very much appreciated.

I know there is a forum for logic and stuff, but not as a subset of homework help, so I'm not sure..

Homework Statement

Give a formal proof for the following conclusion:
$(\neg P \wedge \neg\neg\neg P) \vee P$

Homework Equations

There aren't any premises, so we're supposed to show that the conclusion is logically consistent.

The Attempt at a Solution

Beside the fact that I'm quite new to formal logic and don't really know how to start with this (having tried multiple things), there's something more important that's bothering me: I don't think this conclusion IS logically consistent.

You see, the logical OR is an inclusive-OR, which means that in the above case, you can have BOTH $\neg P$ and $P$. But that makes no sense. Is that correct, or am I missing something? Can you still give a 'formal proof' for any such thing?

Well, I'm not sure about formal proof since you're only given P but...

$(\neg P \wedge \neg\neg\neg P) \vee P$

since there's a triple negation in the second P you can take two of them out, and you get...

$(\neg P \wedge \neg P) \vee P$

So that can be reduced...