I see the symbol used, and I've never seen it logically defined. In words, It's defined as a symbol meaning 'therefore'. Because of a lack of definition, I have no idea why this is false:
A B ∴C
For me, this statemnet could mean one of two things.
'If A and B thus C': (A^B) -> C i.e same as conditional
That ∴ is the same as the conditional, only without a truth value for when the premises is false (conclusions cannot draw upon a false premise) 'A thus B', perhaps? I've read that a valid argument is only so if it is (logically/symbolically/algebraically) impossible that the conclusion be false, given that premise is true.
I am not certain on that, and any correction would be appreciated. However, regardless, I still can't find a strict, logical definition or equivalent of ∴, and it's not that I haven't looked, the ∴ only ever seems to be talked about, never strictly defined.