It is completely backwards, in fact. An argument of the form of P -> C (if premise, then conclusion) is (vacuously) true if P is false, regardless of the conclusion.
Yes, that's exactly right! If you write out an argument in the form of a single logical proposition and any of the premises are false, then the proposition itself is true.
That's one of the things they beat into your head a lot in Logic 101 since it's rather counterintuitive that a material conditional with a false antecedent is always true. GIGO.
My only nit would be that terminologically one wouldn't normally use the terms "true" or "false" to describe an argument, since if you did, then you'd have to say that all arguments with a false premise are true, and that's just too confusing. So usually one speaks of arguments in terms of validity and soundness instead.
P.S. Another thing that's confusing to Logic 101 students on day 1, is that an argument can be valid and yet the conclusions can still be false.
In math, this usually doesn't come up, since you wouldn't typically have valid proofs in math that started with a false premise.
> That is just wrong.
It is completely backwards, in fact. An argument of the form of P -> C (if premise, then conclusion) is (vacuously) true if P is false, regardless of the conclusion.