logic - ¬q, (¬p⇒(¬q⇒¬r)), (s∨r), (s⇒t), and (p⇒t), prove t., using Fitch - Stack Overflow

admin管理员组

文章数量:1394544

I am doing an intro to logic course and have been set the above. The rules allowed are:

1. and introduction
2. and elimination
3. or introduction
4. or elimination
5. negation introduction
6. negation elimination
7. implication introduction
8. implication elimination
9. biconditional introduction
10. biconditional elimination

Clearly, I need to prove either s or p, in order to then use implication elimination on p=>t or s=>t.

I am new to this, the course materials are frankly not great, and it's all just book-based so there is no way of talking to an instructor, so I'm struggling a lot to see how this would be done.

Here are some approaches I've thought of

1. Prove that r=>t, so that or elimination can be performed on s|r, r=>t and s=t. I cannot work out how to prove r=>t, but it must rely on showing that r implies p, which implies t. Given the Fitch rules, however, I do not see how this is done.

2. Prove p by showing that ~p=>~r (easy to do), and that p=>r (this is what I can't work out how to do)

Any help would be greatly appreciated! James.

本文标签： logic172q(172p⇒(172q⇒172r))(s∨r)(s⇒t)and (p⇒t)