Sufficient Assumption Help!

poonsterman1
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Joined: Wed Nov 10, 2010 5:08 am

Sufficient Assumption Help!

Postby poonsterman1 » Tue Jul 26, 2011 1:17 am

Hey guys i'm struggling hard with formal logic in sufficient assumption questions, stuff like :

No chordates are tracheophytes, and all members of Pteropsida are tracheophytes. So no members of Pteropsida belong to the family Hominidae.

The conclusion above follows logically if which one following is assumed?
A) All members of the family Hominadae are tracheophytes.
B) All members of the family Hominidae are chordates.
C) All tracheophytes are members of Pteropsida.
D) No members of the family Hominidae are
chordates.
E)No chordates are members of Pteropsida.

I am terrible at these kinds of questions and would like any input you have on how to approach/solve them.

Thanks in advance!

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WhoIsDonDraper
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Re: Sufficient Assumption Help!

Postby WhoIsDonDraper » Tue Jul 26, 2011 1:28 am

So you are looking for the assumption (missing conditional/formal logic sentence) that makes this argument valid. Make sure you realize how this is different from a necessary assumption first. But your title at least indicates that you might already know this.

First with all questions like this separate into premises and conclusion.

Premises:
C--> ~T
P--> T
-----
Conclusion:
P-->~H

Next expand the conclusion of the argument, this is generally what you should try to do with all of these type of questions.

P........................-->..............................~H

Now try to fit in the other premises into this argument (where the dots are) and see where the gap (sufficient assumption).

P-->T --> ~C..........~H

You need to somehow connect ~C and ~H. You can either do that with ~C-->~H or the contrapositive H-->C. You find this in answer choice B. Im sorry if this seems weird, it is the best way I could explain it on the computer.

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rinkrat19
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Re: Sufficient Assumption Help!

Postby rinkrat19 » Tue Jul 26, 2011 1:31 am

I know you're supposed to diagram them with C => -T and whatnot, but for that kind of question, I got better results by drawing a Venn diagram.

No C are T, so the C and T circles are separate.
All P are T, so the P circle is completely enclosed within the T circle.

Conclusion: No P are H, so the H circle is completely outside the P circle, but could still overlap the T circle and/or C circle, or neither.

A) [All H are T] H circle enclosed within T circle, but that doesn't prove whether H overlaps P or not.
B) [All H are C] H circle within C circle, which means that it can't overlap the P circle because no C are P. This proves the conclusion.
C) [All T are P] P circle and T circle are identical, but that doesn't prove anything about where H is.
D) [No H are C] H circle is outside C circle, but doesn't prove if it overlaps P or not.
E) [No C are P] We already knew that. Doesn't help.

:| I think I did that right. It's bedtime.

tomwatts
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Re: Sufficient Assumption Help!

Postby tomwatts » Tue Jul 26, 2011 1:35 am

If you look up what this actually means, it ends up saying that trees don't have spinal chords. I think that's funny.

I basically agree with the conditional chain way of doing this (the first response), so I suppose I don't have anything useful to add, other than to mention that conditional chains are pretty common with this kind of question.

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emkay625
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Re: Sufficient Assumption Help!

Postby emkay625 » Tue Jul 26, 2011 2:12 am

tomwatts wrote:If you look up what this actually means, it ends up saying that trees don't have spinal chords. I think that's funny.


+1

bhan87
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Re: Sufficient Assumption Help!

Postby bhan87 » Tue Jul 26, 2011 2:29 am

One critical step you should take for sufficient questions is to plug your answer choice back into the argument. The correct response MUST completely fix the argument. You'll also want to refer back to Powerscore's section on conditional reasoning because many of these questions are damn near impossible to answer without having a deep understanding of how to diagram conditional statements.

WhoIsDonDraper correctly states that you need to understand how sufficient assumptions differs from a necessary one. Necessary assumptions are (unsurprisingly) assumptions that must be true in order for the conclusion to be valid, but that doesn't mean that the assumption alone will complete the argument. Sufficient assumptions in themselves can complete the argument, but it's not always the case they are needed for the conclusion to be valid.

An example: Jim has 50 cents in his pocket.

Necessary assumption: Jim has more than 20 cents in his pocket (this MUST be true in order for him to have 50 cents, but the fact that he has 20 cents is not enough to conclude he does have 50 cents).

Sufficient assumption: Jim has 2 quarters in his pocket (this in itself can make the conclusion valid, but it's not necessarily the case that this assumption is necessary because Jim could have 5 dimes, or 10 nickels, etc.)

poonsterman1
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Re: Sufficient Assumption Help!

Postby poonsterman1 » Wed Jul 27, 2011 12:08 am

Thank you for the responses guys, most of it has been helpful so far. One last thing, what is your particular method for attacking these questions, is it: 1. find conclusion 2. find premises and try to connect? If i had to isolate my problem, i'd say it has to do with being confused with how to order the premises in order to make the chain work, and i was also wondering how you guys did it.

Any further input would be greatly appreciated :D

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KevinP
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Re: Sufficient Assumption Help!

Postby KevinP » Wed Jul 27, 2011 12:22 am

poonsterman1 wrote:Thank you for the responses guys, most of it has been helpful so far. One last thing, what is your particular method for attacking these questions, is it: 1. find conclusion 2. find premises and try to connect? If i had to isolate my problem, i'd say it has to do with being confused with how to order the premises in order to make the chain work, and i was also wondering how you guys did it.

Any further input would be greatly appreciated :D


My method is usually finding the core of the argument. Find the premises, find the conclusion, and link them together. Then look for any gaps.
Oh, if you haven't already, take a look at Powerscore's Logical Reasoning Bible or Manhattan's Logical Reasoning Guide. Both are superb resources with my personal preference leaning towards Manhattan's LR guide.




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