[ealhad]

I don't understand.

If A implies B, then not B implies not A, and I'm pretty sure when I was in CS school in France (5 years ago) we learned this.

And I'm also pretty sure that I knew this before, though I can't exactly remember when I first learned it.

[lkbm]

Modus tollens. It was also covered in both CS (explicitly in Discrete Math) and Philosophy (explicitly in Intro to Logic, and implicitly in many others) at my school in the US.

It seems like the question in the article doesn't really make it clear that you're supposed to answer about the relation between the two. It could easily be interpreted as a question about the truth value of each.

It's definitely true that some people don't think in terms of formal logic and wouldn't know this anyway (this is why we have affirming the consequent and denying the antecedent as common examples of bad logic), but I don't think the question as stated demonstrates that of them.

EDIT: Just remembered it being explicitly explained in Intro to Philosophy and/or Professional Ethics as well.

[lkbm]

One amusing thing I saw in the two courses I mentioned is that in Intro to Logic, we spent something like a month learning each of the eighteen rules of inference, gradually adding a couple each day until we were familiar with all of them.

In Discrete Math, the professor wrote out the eighteen rules in as part of a single lecture and then we had homework due that same week wherein we were expected to know and use all of them. (He may have introduced predicate logic in that same lecture.)

Intro to Logic was a philosophy course, but some majors allowed students to take it instead of their one required College Algebra course. The result was it was a lot of very non-technical people who struggled with intro algebra, and consequently struggled with formal logic. (Predicate logic was the focus of the third section of the course later on.)

Discrete Mathematical Structures was a math/cs course, where almost every student was a CS major, so it was predominantly technically-minded people for whom formal logic was at least very familiar, if not natural.

[pico303]

I think it's a trick question, in the way he phrases it. If A implies B, then not B implies not A. But he doesn't say that. He says, "If A implies B, does not A imply not B," for which the answer is no.

[whoisburbansky]

The way he phrases it is "What can we say about !A and !B," according to the article. The only time he talks about "If A implies B, does not A imply not B," is when describing close answers he got to his question. I don't think it's a trick question the way he asks it, and it also seems like the sort of thing you should be able to work out with concrete examples if you aren't sure.

[teorema]

God I feel like an idiot for questioning this, but is it really true not B implies not A in that situation? It seems like it depends on what you mean by "implies."

E.g., you could have A -> B, and A -> C, and B != C. Then C is not B, but implies A just as much as B might (in the very least it doesn't imply not A per se, as A might be true). It seems like there's some implicit assumptions going on.

[lpellis]

If A implies B (A -> B) then you cannot have A -> C Unless you meant it can imply both, but then still A implies B.

A dog (A) has 4 legs(B). Something that does not have 4 legs (not B) is not a dog (not A). A cow though (not A) could still have 4 legs

[_y5hn]

A dog can have 3 or less legs.

[falseprofit]

"not B" doesn't mean "something else which is not identically B", it means "the negation of B". Also, the statement "A->B" has absolutely no bearing on the statement "B->A". Hope this helps.

[ealhad]

Well, no, he asks "What can we say about `not A' and `not B'?"

[pico303]

Ah, sorry. You're right.

[chrisweekly]

Yet, your answer was the complete and correct answer!