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I want to formalize and proof the validity of "If I train or if I don't train if and only my friend competes, I'll go to the meeting"

  • p = I train
  • q = my friend competes
  • r = go to the meeting

My guess is (p ∨ (¬ p ↔ q)) → r, but I'm not sure about what "if and only" means in this case.

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  • $\begingroup$ i have no idea how to parse that phrase. Don't even know what "I'll go to the evening" means. I expect there is a language issue here. $\endgroup$
    – lulu
    Jun 3 at 11:23
  • $\begingroup$ What does it mean "if and only"? We have "if and only if". $\endgroup$
    – Mauro ALLEGRANZA
    Jun 3 at 12:42
  • $\begingroup$ That is exactly my question. This is directly copied from an exercise. Maybe there is a typo in the question itself? And if we suppose that they made a typo and the correct phrase is: "If I train or if I don't train if and only if my friend competes, I'll go to the meeting", is my solution correct? $\endgroup$
    – Lita
    Jun 3 at 12:56
  • $\begingroup$ My best guess to fix the broken question is to turn "if and" into "and if". It then becomes meaningful but ambiguous English, probably intended to to mean $(p \lor (\lnot p \land q)) \to r$ (where $q$ means "only my friend competes"), suggesting that you don't think you need to train to beat your friend. However, your interpretation and mine are not valid without further assumptions. $\endgroup$
    – Rob Arthan
    Jun 3 at 19:36
  • $\begingroup$ Thank you for your help! $\endgroup$
    – Lita
    Jun 5 at 21:59

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