No, what he’s written is correct[0]. A ∨ B, ¬A ⟶ B, and ¬B ⟶ A are all equivalent. (Hence your last statement is also correct!) Note for instance that the last two are just contrapositives of one another and so equivalent.
[0]In classical logic, obviously, for the nitpickers; that’s all I’m going to consider here.
Note also you could easily see your initial comment to be wrong just by computing the truth tables! Equivalence in classical propositional logic is pretty easy—you don’t need to think about proofs, just write down the truth tables!
No, what he’s written is correct[0]. A ∨ B, ¬A ⟶ B, and ¬B ⟶ A are all equivalent. (Hence your last statement is also correct!) Note for instance that the last two are just contrapositives of one another and so equivalent.
[0]In classical logic, obviously, for the nitpickers; that’s all I’m going to consider here.
Ah, of course. Thanks.
Note also you could easily see your initial comment to be wrong just by computing the truth tables! Equivalence in classical propositional logic is pretty easy—you don’t need to think about proofs, just write down the truth tables!