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Syllogism is defined as:

"All A are B", and "All C are A", thus "All C are B".

For example:

"All birds have features", "Penguins are birds", thus "Penguins have feather"

How do we represent this logic in mathematics? To which mathematical branch it belongs?

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    It seems you already knew the answer to your last question when you chose the tag? :-)2011-07-22
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    No @joriki. I just didn't know what tag is suitable for this question, and I couldn't also post the question without tags. :)2011-07-22
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    Well, you got that one right; this belongs to logic.2011-07-22
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    BTW, you do know that the body covering whose presence is characteristic of birds is spelled "feather", not "feature", right? Although, certainly, being feathered is indeed a typical feature of birds...2011-07-22
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    BTW, not all syllogisms (no pun intended) are of the form ("all a are b..."), i.e. it is not necessary that the three propositions are "positive/universal". http://en.wikipedia.org/wiki/Syllogism#Types_of_syllogism2011-07-23

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