formal logic help PLEASE!! some all most quantifier problems are killing me!

[Angelica]

Formal logic problems with quantifiers - some most all none many several few - and all that are killing me!!!!  I try to diagram them but get messed up with how it works when you put some with all or some with most and the combinations.  Some with an all works one way but doesn;t work the other way?  I'm confused about that.  Thought I had it down before but I forgot or had it wrong or something.  I keep missing inference, must be true, paralell reasoning, justify and other questions that have this stuff in them.   HELP!!!!

Did #43 June 2004 prep today and got killed by #17 in section 1, the one about UN countries.  All the answers say some and talk about things in the question and seem kinda right.  I tried to diagram it but got waaaaayyyyy lost and frustrated.   
How do I do this one? 

[LSATEnthusiast]

While clearly this a question with formal logic, it helps to keep things simple and not worry about over-diagramming:

The first sentence tells you about countries permanently on the UN Sec. Council: they're not small and they're not in the southern hemisphere.
The next sentence tells you something else about those countries: they favor more peackeeping efforts and more UN involvement.

While we now know quite a lot about these Sec. Council countries, what do we know about countries NOT on the Sec. Council? Nothing. They may be small or large. They may be in the north or south. They make have any opinion on peacekeeping efforts and UN involvement.

The last sentence is a big red herring. It tells you that some countries that favor more peacekeeping efforts are against increases spending on refugees. However, which countries are they? Are they the ones on the UN Sec. Council, or are they other countries? We don't know for sure. Therefore, there is really no 100% connection between this sentence and the previous two.

At this point, knowing what you know, check out the answers:

(A) Possible, but we don't know anything about small countries other than that they're not on the UN Sec. Council.
(B) Again, we don't know anything about southern hemisphere countries other than that they're not on the UN Sec. Council.
(C) Clever answer. However, we don't know if any of the Sec. Council members are among of the countries referenced in the last sentence.
(D) Same problem as (A).
(E) Bingo! We know the five members of the Seucirity council favor greater UN involvement, and we know they're not in the southern hemisphere. Those five nations fit the description in (E), so we know those countries must exist.

HTH

- Chris

[LSAT Eliminator]

Good answer!

[Trainwreck]

Powerscores LR LSAT Bible has a good section on formal logic problems. They're not easy no matter what you do tho.

[Ashley O]

One thing to keep in mind is that formal logic doesn't appear that much on the LSAT, so you won't see too many of these problems when you take the test

[Jeffort]

Chris/LSAT Enthusiast's explanation is good for explaining the logical justification behind the credited answer choice, it gets right to the point of why (E) must be true based on the premises in the stimulus.  

I'm going to expand because this problem is a good one for LSAT instructional purposes about dealing with formal logic premises, combining them, and differentiating valid versus invalid conclusions from the various available transitive combinations.

Forgive me if this is overkill/overly complicated for just solving the problem itself.  Here goes...

As with most must be true questions, the stimulus is just a set of facts rather than an argument and your job is to find the answer choice that states a valid conclusion that can be logically concluded from the offered facts/premises.

Given the set of conditional/formal logic premises presented here and the number of available valid conclusions that can be drawn from combining them, it is impossible to pre-phrase or anticipate which valid conclusion to specifically look for in the answer choices before reviewing them.  There are several other available valid conclusions that MUST BE TRUE which LSAC could have instead included as the credited answer choice.


Breakdown of the question:  PrepTest #43, June 2004 #17 LR section #1

Abbreviation of the conditional elements:

SC = small countires
SH = southern hemisphere
PUNC = permanent seat on UN security council
IPC = in favor of increased peace keeping efforts
GRMD = greater role in moderating regional disputes
$R = in favor of increased spending on refugees (in the negated form ~$R = against increased spending)


Premises presented in the stimulus:

SC OR SH    ~PUNC
contrapositive:  PUNC   ~SC AND ~SH

PUNC    IPC AND GRMD
contrapositive:  ~IPC OR ~GRMD   ~PUNC

IPC   ~$R


If you accurately diagrammed all three premises before heading to the answer choices you should recognize that they share several common elements and can be put together with the transitive property.

PUNC    IPC  AND GRMD AND ~SH AND ~SC
along with:  PUNC    IPC   ~$R

Now that is a fairly complex and confusing set of conditional combinations.

The reduced (diagram excludes the elements the answer choice does not talk about/need/depend upon) combination of them that proves answer choice (E) MUST BE TRUE is the contrapositive of the 1st premise and the original form of the second premise:

PUNC   GRMD AND ~SH

With this problem could you have anticipated that as what to look for in the answer choices after diagramming the stimulus, inspecting for valid transitive links and before spot checking the answers?  

NOOOOooooooo!    

Since all PUNC are GRMD and ~SH , there will be a   overlap between those two necessary conditions that must be true.  
Since countries that are PUNC exist ('Each of the 5 countries...' -second sentence of stimulus-), every country in that group shares those two necessary conditions, therefore it must be true that:

GRMD   ~SH  and you have proven that (E) MUST BE TRUE!  

Even though the CR does not mention countries that have a permanent seat on the UN security council, you need to analyze from PUNC and know what logically follows about countries that have a PUNC to get it and be certain about the credited answer.


However, there are several other available MUST BE TRUE transitive conclusions that follow logically from the premises that could instead have been listed as the correct answer.

IPC   GRMD
IPC   ~SH
~SC   ~SH
~SC   GRMD
~SC   IPC

This question could have been even nastier if LSAC had decided to make it a MUST BE TRUE EXCEPT question since there are more than four MBT conclusions that the premises in the stimulus prove to be logically correct.

(If I was the LSAC question writer behind this one and was having a bad day and in a bad mood at the time I might very well have advocated to make it a MBT Except question!)