[phonebanshee]

Except that it also depends on the definition you're using for "implies," so the normal use of English breaks things if you're really asking about logic. For example, dog implies "likes dogfood" is a reasonable thing to say, but "doesn't like dogfood" certainly includes dog outliers who only eat, say, kitchen scraps, and refuse dogfood. So no, a implies b doesn't let you say not a implies not b, given the normal definition of "implies."

I suspect though that this is the kind of quibbling that will quickly pass the interview test; you say something about dogfood and colloquial use of _implies_, the interviewer says "oh no, we're talking about formal logic where implies means..." and you go on from there. And frankly, that's the kind of interview question that's useful, since if you assume that marketing people use the logic definition of "implies" you're going to be in all sorts of pain in real-world meetings about developing software.