Logic games neither/nor

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Logic games neither/nor

Postby mistd » Wed Jul 31, 2013 10:45 am

I have been scouring the Internet to get this right and I think this is it:

Original:A--> B+C
Contrapositive: ~B or ~C -->~A
The contrapositive means: if neither B nor C are picked then A is also not picked. Simply put, if BOTH B&C are not chosen, A is not chosen.
Is this right? Could it also mean that if B OR C(just one of them)is not chosen, A isn't chosen?
Also what about in the case of ~B &~C -->~A? This definitely means if B AND C are both not chosen A is not chosen. Isn't this the same as the contrapositive example above? If so, is there really a point in distinguishing them in these types of cases?
I'd really appreciate the help, I am growing quite desperate.

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Re: Logic games neither/nor

Postby Cambridge LSAT » Wed Jul 31, 2013 1:25 pm

Your diagram for the first case is correct, but your initial interpretation needs clarification. We don't need to know that BOTH B and C are out to infer that A is out; one of B and C being out is sufficient.
Original: A → B and C
Contrapositive: ~B or ~C → ~A

The contrapositive means that if either B or C (or both) is out, then A is out.

You can also split the rule into two parts if it makes it easier to read:
A → B; ~B → ~A (contrapositive)
A → C; ~C → ~A (contrapositive)

The second case you mentioned ~B and ~C → ~A is distinct from the example above. In this case, because the sufficient condition has two parts which can't be separated, it's only triggered when both B AND C are out.

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Re: Logic games neither/nor

Postby mistd » Wed Jul 31, 2013 1:46 pm

Thank you so much!
Officially my favorite person (company) of the day!

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Re: Logic games neither/nor

Postby Clearly » Wed Jul 31, 2013 1:56 pm

Your confusion seems to lay in the phrase neither nor. just translate the phrase by thinking about what it means
If a neither b nor c
If a no b, and no c

Contra we always switch and to or and or to and.
B or c > ~a

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Re: Logic games neither/nor

Postby TylerJonesMPLS » Sat Aug 03, 2013 1:40 am

There are really two issues here.

One is how to get the contrapositive of a conditional when the sufficient condition and/or the necessary condition contains more than one proposition.

The other issue is the logical meaning of “or.”

The rules for the first issue are called DeMorgan’s Laws. You can google for them and get the rules and full explanations.
You got your example exactly right according to DeMorgan’s Laws.
A ---> (B & C) then the contrapositive is (~B or ~C) ---> ~A

You got confused over the logical meaning of “or” But don’t feel bad about it. Everyone gets confused about this. The most common everyday meaning of “or” is called “exclusive or”. If you go to a restaurant and the menu says you can have soup or salad with your entree, you naturally interpret that to mean that you can have your entree with soup (but not salad) or you can have your entree with salad (but not soup). But you can’t have your entree with both soup and salad.
The kind of "or" used in logic is "inclusive or". Inclusive "or" means: you can have your entree with just the salad (and not the soup) ; you can have your entree with just the soup (and not the salad) ; you can have your entree with both the salad and the soup.
You have probably seen the expression “and/or”. That is another way, and a clearer way, of using “inclusive or” : With your entree, you can have the salad and/or the soup.

This is one of the nasty tricks of the LSAT. They use “or” in the sense of “inclusive or” which is the way that “or” is used in logic, but not in ordinary life. And the LSAC does not ever tell you that “or” always means "inclusive or" on the LSAT!

So, you got the correct contrapositive:
(~B or ~C) ---> ~A
Since the “or” is “inclusive or”, this is what the contrapositive means:
~B ---> ~A ; ~C ---> ~A ; (~B & ~C) ---> ~A

If you google for “inclusive or” and “exclusive or” and “does the LSAT use inclusive or?” you will get back a bunch of hits explaining this all in great detail.

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