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Need Help for Syllogism problem

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Need Help for Syllogism problem  [#permalink]

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New post 09 Oct 2018, 10:24
All men are dogs.
All dogs are cats.

given conclusions : I) All men are cats. II) All cats are men.


I solved above question but the real answer is given as Only conclusion I) follows.

But when I solved what I got is as follows:

1) First I took converse of both the premises :
Some dogs are men
Some cats are dogs

Here , both the premises converse hold.


2) Then I took middle term i.e dogs and checked that dogs is distributed once in the premises.

3) Since both the premises are affirmative so the conclusion must be affirmative according to the rule. Hence
conclusion should be => All men are cats . The converse also holds true i.e All cats are men. Hence according to me I get answer as
Both Conclusion I) and II) follows. But it is not matching with the answer given in my textbook. Please help me.
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Re: Need Help for Syllogism problem  [#permalink]

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New post 09 Oct 2018, 13:01
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Hi Amoghsingh,

The concept that you're interested in is referred to as 'formal logic' - and in this case we're also discussing a "contra-positive", which defines a statement that is logically equivalent to another statement. This subject is a specific area that occurs on the LSAT, but exceedingly rarely on the GMAT. Thus, if you're actually studying for the GMAT, you should NOT be wasting your time on this concept. Here is the basic idea though: to form a contrapositive, you must reverse the order of the elements and put the the word NOT in front of both.

"All women are humans."

There is a statement that is logically-equivalent (the contra-positive) which would be:

"If you are NOT a human, then you are NOT a woman"

The statement "All humans are women" is NOT logically correct though. Formal logic goes in "one direction" and you cannot simply reverse the pieces and form a logical statement unless the two subjects form the exact same group.

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Re: Need Help for Syllogism problem   [#permalink] 09 Oct 2018, 13:01
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