vacuous truth

nobody17
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vacuous truth

Postby nobody17 » Mon Aug 05, 2013 12:51 am

Suppose we had this game on the LSAT:

There will be 6 concerts in sequential order. Exactly six bands, A, B, C, d, e, and f, will perform. Each band performs exactly once, and exactly one band performs at each concert. The assignment of bands to concerts follows the rule below:

- No band whose name is a lower case letter will perform at the concert immediately following the concert at which B plays.

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My question is: does this then imply that there must be at least one concert that follows the one that B plays at, ie: B cannot play at concert 6? It seems to me that you could assign B to concert 6 in which case the rule is vacuously true. Sorry for not providing an actual LSAT question to demonstrate this question, but hopefully the idea is still conveyed here.

Thanks!

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Balthy
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Re: vacuous truth

Postby Balthy » Mon Aug 05, 2013 1:16 am

B would still be able to play at 6. If it were the other way around ("B must be played immediately before a lower case letter") then B could not play at 6. I have even seen a few instances of something like "B must be played immediately before a lower case letter, unless B is last."

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clay7676
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Re: vacuous truth

Postby clay7676 » Mon Aug 05, 2013 1:18 am

No I don't think it is "vacuously" true. It means exactly what it says in my estimation. There must be other rules that give more merit to that rule, but you can note that whenever there is a Big B there will never be a small letter (that seems pretty important for sequencing the order), but it doesn't have to necessarily force an inference directly about the order. B certainly could be in 6 based on that rule alone, too.

nobody17
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Re: vacuous truth

Postby nobody17 » Tue Aug 06, 2013 1:34 am

Thanks for the replies so far. I have to admit, now I'm a bit confused. The question came up as I was working through the Manhattan LG prep book. In one of the practice games they created, they have the following rule:

"There will be no opening act at the concert immediately following the concert at which F plays."

and then their solution diagram infers that F cannot play at the 4th concert (there are 4 concerts in total). Looking at all the rules, I'm pretty sure it's the above rule working alone that leads them to draw that inference (I'd post the entire game but I'm not sure what the policy on that is). I'll see if I can find an actual LSAT question where this comes up, in which case at least I have a reference solution.

clay7676: I think you may have misunderstood me. I was saying that the rule about the bands is vacuously true if B plays at 6 (there are no more concerts after 6, so anything you say about them will be true).

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Clearly
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Re: vacuous truth

Postby Clearly » Tue Aug 06, 2013 1:41 am

On an entirely unrelated side note, LG's never use A B C D or E as characters, presumably to not confuse people as to the answer choice letters. LSAT trivia for the day.

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LSATSCORES2012
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Re: vacuous truth

Postby LSATSCORES2012 » Tue Aug 06, 2013 2:06 am

nobody17 wrote:Thanks for the replies so far. I have to admit, now I'm a bit confused. The question came up as I was working through the Manhattan LG prep book. In one of the practice games they created, they have the following rule:

"There will be no opening act at the concert immediately following the concert at which F plays."

and then their solution diagram infers that F cannot play at the 4th concert (there are 4 concerts in total). Looking at all the rules, I'm pretty sure it's the above rule working alone that leads them to draw that inference (I'd post the entire game but I'm not sure what the policy on that is). I'll see if I can find an actual LSAT question where this comes up, in which case at least I have a reference solution.

clay7676: I think you may have misunderstood me. I was saying that the rule about the bands is vacuously true if B plays at 6 (there are no more concerts after 6, so anything you say about them will be true).

If B is 6th then it is true that "No band whose name is a lower case letter [is] peform[ing] at the concert immediately following the concert at which B plays." That's all that matters.

Vacuous truth isn't a necessary concept for the LSAT and it will confuse you. It is not necessary to employ here.

Regarding the rule you've given... given the following rules:

1. Set A B c d
2. There will be no lowercase letter immediately following A

It does not follow that A cannot be fourth.

Consider the following sequence: BcdA. If I were to ask you the following question: is there a lowercase letter immediately following A? - what would your answer be? It would surely be no, which fulfills the criteria that we are given. In order to reach the conclusion you've proposed, there must be some additional rule.

Hat Trick
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Re: vacuous truth

Postby Hat Trick » Tue Aug 06, 2013 2:20 am

Clearly wrote:On an entirely unrelated side note, LG's never use A B C D or E as characters, presumably to not confuse people as to the answer choice letters. LSAT trivia for the day.


Not true. PT5, S2, G1

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Clearly
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Re: vacuous truth

Postby Clearly » Tue Aug 06, 2013 2:22 am

Hat Trick wrote:
Clearly wrote:On an entirely unrelated side note, LG's never use A B C D or E as characters, presumably to not confuse people as to the answer choice letters. LSAT trivia for the day.


Not true. PT5, S2, G1

Ok, logic games almost never, and haven't in 20 years used ABCDE as characters :roll:




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