I am doing an intro to logic course and have been set the above. The rules allowed are:
- and introduction
- and elimination
- or introduction
- or elimination
- negation introduction
- negation elimination
- implication introduction
- implication elimination
- biconditional introduction
- 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
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.
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.