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Comments on Prove that $A \leftrightarrow \lnot\lnot A$ (WIP)

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Prove that $A \leftrightarrow \lnot\lnot A$ (WIP)

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Task

Prove that $A \leftrightarrow \lnot\lnot A$ using only the following axioms:

  1. $P \rightarrow (Q \rightarrow P)$
  2. $(P \rightarrow (Q \rightarrow R)) \rightarrow ((P \rightarrow Q) \rightarrow (P \rightarrow R))$
  3. $(P \rightarrow Q) \leftrightarrow (\lnot Q \rightarrow \lnot P)$

Scoring

Your score will be the number of times you apply any of the axioms above.

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1 comment thread

Which rules of inference are allowed to be used? (2 comments)
Which rules of inference are allowed to be used?
celtschk‭ wrote about 3 years ago

Which rules of inference are allowed to be used?

I expect modus ponens is one of them. Also, given that you don't give any axioms for $\leftrightarrow$, you'll need to allow some rules of inference for that as well.

user‭ wrote about 3 years ago

celtschk‭ I'm really sorry, but I'm not sure what exactly rules of inference are, I've kinda given up on this draft because I don't know enough logic to make it work. Feel free to post a version of it yourself if you want, though.