/sci/ - Science & Math

I'm in a babby logic course, and one of our units is doing simple proofs. But before learning that, we had to practice converting English sentences into propositional-logical symbols.

One such question was
>The Australians will either capsize or win the race, but if they capsize they won’t win.

While an obvious answer is (C∨A)•(C⊃~A), I simplified that to C ⊻ A.

However, it was marked as wrong, on the basis that " '⊻' is not part of our logical language."

I was pretty sure that the "exclusive or" is part of propositional logic, and that it can be denoted by ⊻. Plus, I think my translation is more succinct and elegant than the conjunction.

So, if ⊻ is not from propositional logic, what sort of logic is it from? So far, we've only looked at categorical (Aristotelian and Boolean) and propositional.

Just out of curiosity, what are the different logical languages, and what are the differences between them?

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