I love logic games.
Published by Talula April 18th, 2005 in lawOr at least I’m trying to. I hear it’s more fun than the logical reasoning section (yes I’m studying for the LSAT) and anyway if you have fun then you’ll do better, right? So. Read on if you feel like putting your brain through some calisthenics.
I think there is something wrong with this question. I’m hoping someone will read this and understand what it is that I’m missing, and explain it to me. Either that, or sympathize with me that the book is flawed and I am the genius who should be writing these damn things. The question is from page 133 of the LSAT Logic Games Bible by Powerscore. It goes like this:
“Bird-watchers explore a forest to see which of the following six kinds of birds–grosbeak, harrier, jay, matin, shrike, wren–it contains. The findings are consistent with the following conditions:
If harriers are in the forest, then grosbeaks are not.
If jays, martins, or both are in the forest, then so are harriers.
If wrens are in the forest, then so are grosbeaks.
If jays are not in the forest, then shrikes are.”
Then there are a whole slew of questions, but the one that gets me (the most) is this:
“If both martins and harriers are in the forest, then which one of the following must be true?
(A) Shrikes are the only other birds in the forest.
(B) Jays are the only other birds in the forest.
(C) The forest contains neither jays nor shrikes.
(D) There are at least two other kins of birds in the forest.
(E) there are at most two other kinds of birds in the forest.”
(I love logic games. I love logic games. Really I do. I love them.)
So I’m thinking this.
If there are martins and harriers, then there must be no grosbeaks or wrens. (By rules 1 and 3, respectively.)
We are left with only shrikes and jays, and we can only have one or the other, not both, and not neither.
If you’re still with me, check this. This is what the explanation of the answer says, after making my first inference (but, my main confusion, not second):
“The only unaddressed birds are S and J, and at least one of them, possibly both, must be in the forest. Answer choices (A) and (B) are therefore incorrect because it is possible that both the S and J can be in the forest. Answer choice (C) is incorrect because, due to the final rule, the forest always contains at least S or J. Answer choice (D) is incorrect because it is possible there is only one other kind of bird in the forest (S or J). Answer choice (E) is thus correct since at most S and J can be in the forest in addition to M and H.”
What??!?!?!?!! I thought that the final rule stated that either S or J, but not both, could be in the forest. From “If not J, then S” follows the contrapositive, “If not S, then J.” (Contrapositive means that you can get from “if x then y” to “if not y then not x.”) What am I missing? Will someone please fry some of their brain with me. It’s a lonesome cookout over here.
6 Responses to “I love logic games.”
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Well, thanks to 4 we can make two statements:
if not j then s
if not s then j
however, since we do not have ‘if j then not s’ or ‘if s then not j’ statements it is possible to have both s and j. I thought about it in a more wordy situation:
If Jays clear out of the forest, then Shrikes will move in to replace them. If the Shrikes later move out, then the Jays will come back. However, if the Jays, say, get real hungry, they COULD come back early and fight with the Shrikes for the food.
I could be way off, but it seems clear to me.
Gary Curtis, author of http://www.fallacyfiles.org/index.html, replied to my request for a comment to this entry via email. I’m posting his reply here. Together with Mikeal Peterson’s answer, I think I understand where I’m going wrong. Tricky that it’s so counterintuitive for me. Thanks for replies.
Talula,
The problem appears to be correct to me. I think you’re getting
confused when you say:
“We are left with only shrikes and jays, and we can only have one or
the other, not both, and not neither” and “I thought that the final
rule stated that either S or J, but not both, could be in the forest.”
The final rule–which I assume is the one that says “if jays are not in
the forest, then shrikes are”–does say that either jays or shrikes are
in the forest, but it doesn’t say that both are not. All the rule says
is that IF jays are not there, then shrikes will be. It doesn’t say
what happens if jays ARE there; for all we know from the rule, shrikes
might be there, too.
What you say about contrapositives is right, but not really to the
point. I suspect that you’re reading the rule to say “if and only if”,
which would make it true that not both jays and shrikes are in the
forest. Confusing “if” and “if and only if” is a common mistake.
Hope that helps.
Good luck on your LSAT. When are you taking it? June?
Navid, yes, I’m taking it in June. If I can light a fire under my butt and study some more. Lately I’ve been procrastinating by teaching myself to write devanagari script. I’m turning procrastination into a full time occupation. It’s great. Are you taking it too?
Procrastination is the mother of invention!
I’ll bet if somebody told you you had to master devanagari by June, you’d start studying for the LSAT.
P.S. Learning devanagari at home in the States is hard. Learning it on the street in India is easy. You only have to see the English names of tailor shops and sweet emporiums rendered in devanagari a few times before it all clicks into place.
my dear talula,
you are overcomplicating the last rule - it doesn’t say that jays and shrikes cannot coexist - it merely says that if one is not there, then the other will be. ie, at all times there are either jays or shrikes - or both, which is implied - but never the complete absence of jays AND shrikes. get it?
i love me some logic games too