A. Some spades are not clubs
B. No diamond is a spade
C. Some diamonds are spades
D. Some clubs are not diamonds
E. All spades are clubs
F. Some clubs are diamonds.
1)AFC 2)DBE 3)BAF 4) DEA
The above set contains 6 premises followed by 4 answer sets. One of the answer contains the correct logical ordering of the premises, but not certainly in the given order. For eg: If you take AFC (1), AFC can be logically correct or ACF may be or FAC may be, but we clueless about the sequence.
Now my question is how to find quickly wheather which possible set is correct, without going maximum number of checkings. Please help me out.
Note: This is not a homework question, this is a part of problem to be solved in the competetion examination.
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Hi Infinity08,
i mean to say that if you consider the option (1)AFC, it is not compulsory to have the order as A(major) F(minor) and C(conclusion), it might be F(major) C(minor) A(conclusion). Seems that about 6 patterns could be formed. Hope you are clear now. The options hold only the premises which would have some logical conctives and not the it is not guranteed about the order.
>> A(major) F(minor) and C(conclusion)
This changes a lot :) It was my understanding of your question that all three were premises, with a conclusion to be made.
For the new understanding :
take these symbols :
E -- there exists a (i know it should be inverted for the correct symbol :))
A -- for all (same remark :))
: -- for which
! -- not
s : spade
c : club
d : diamond
A) Some spades are not clubs --> E s : s != c
B) No diamond is a spade --> A d : d != s
C) Some diamonds are spades --> E d : d = s
D) Some clubs are not diamonds --> E c : c != d
E) All spades are clubs --> A s : s = c
F) Some clubs are diamonds --> E c : c = d
Now,
1) AFC : All three premises are with E (there exists a) - no sensible conclusion can be made using two of those premises, since the three premises involved are for 3 separate "suits".
==> 1) can't be a solution
2) DBE : Both theses with A (for all) need to be premises, while the these with E (there exists a) needs to be the conclusion.
You can't have a conclusion with A (for all) from a premise with E (there exists a) and one with A (for all).
Now : from B and E we get "A d : d != c", from which we can derive "E c : c != d", which is these d.
==> 2) has this solution : B, E -> D
3) A these with A (for all) can't be a conclusion if both premises are with E (there exists a).
So, B needs to be a premise.
Now : from B and A you can't conclude anything about clubs, so F can't be a conclusion.
from F and B, you can conclude that "E c : c != s" or "some clubs are not spades", which is not the same as A
==> 3) is not a solution
4) DEA : A and E conflict
==> 4) can't be a solution
Hi Infinity,
Thanks for your immediate response. You answer is cool and maked the right one. (2). I would like to know more about your steps. The symbolics you have used seems to be easier than the method taught to me. i.e to find the distribution and non-distribution in the subject and predicate using the below table and applying the principle rules.
Subject Predicate
Universal Affirmative Yes No
Universal Negative Yes Yes
Particular Affirmative No No
Particular Negative No Yes
Can you help me in the symbolic style solving?
You asked earlier if it's possible to work out with Venn diagrams. That is entirely possible, and maybe even recommended to start out on this kind of problem, because it'll give you a better insight. Here's some nice intros to using Venn diagrams for categorical syllogisms like this :
http://philosophy.lander.e
http://www.philosophypages
The symbols i used are just a more formal (short-hand) notation of the same principle. If you're interested, here's a short intro on the symbols i used, and how to use them (more formally than i did in my earlier post) to tackle syllogisms :
http://matcmadison.edu/ale
ie. the universal quantifier A (inverted !!) and the existential quantifier E (inverted !!)
The Venn diagram method will, as i told before, give you more insight into these kind of problems. Once you have the insight needed, the notation used won't matter that much any more, because they basically represent the same. Then indeed, the symbolic notation will be faster, just because you don't need to make drawings ...
The reasoning however is the same. It's just a notation.
The same site i mentioned earlier (but now the main syllogism page) is a good intro to syllogisms :
http://philosophy.lander.e
And for the symbolic notation, check this page :
http://matcmadison.edu/ale
of which i referenced chapter 3 earlier.
What other references are you talking about ?
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by: Infinity08Posted on 2005-09-25 at 21:54:25ID: 14956453
1) find contradicting premises, and eliminate all answers that contain contradicting premises :
a. A and E can't both be true, so that eliminates answer 4.
b. Same for B and C, but there's no answer containing both.
2) Take the remaining answers and test them in the order they're given :
a. AFC poses no problem at all
b. D means "some clubs might be diamonds" coupled with B "no diamond is a spade" and E "all spades are clubs", which leads to "some clubs might not be clubs", which is obviously false --- this solution set includes a possible problem.
c. Same reasoning for BAF, which has as included premise : "some spades might be diamonds, while no diamond is a spade"
NOTE : that is took "some" very literally : meaning that it doesn't say anything about the rest ... eg. "some clubs are not diamonds", doesn't mean that the other clubs ARE diamonds. If that was not intended by the question askers, then the solution is different.
So, a would be my answer, although i'm not sure i got the essence of the question. What is "the correct logical ordering of premises" ? And why is this there : "but not certainly in the given order".