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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 no
by pico303 6y ago
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.
- ealhad 6y agoWell, no, he asks "What can we say about `not A' and `not B'?"
- pico303 6y agoAh, sorry. You're right.
- chrisweekly 6y agoYet, your answer was the complete and correct answer!
- whoisburbansky 6y agoThe 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 6y agoGod 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 6y agoIf 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
- loopz 6y agoA dog can have 3 or less legs.
- falseprofit 6y ago"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.