I have problem with the following syllogism.

Some A are B
All B are C
Some B are C
Some A are C

I think both are correct answers while my book says that the only correct answer is "some A are C".

  • 1
    Of course, Some B are C follows from All B are C... But the syllogism derive a conclusion from both premsies. The rules for syllogism states that the "middle" term (B) will not be present in the conclusion, that must "specify" the relation betwee the "extremes" (A and C). – Mauro ALLEGRANZA Nov 25 '16 at 11:15
  • So what is the correct answer? I am confused by what the middle term in general is – Jerry K Nov 25 '16 at 11:18
  • The correct answer is "Some A are C". See Syllogism : Examples : Darii. – Mauro ALLEGRANZA Nov 25 '16 at 11:23
  • some b are c is correct, but not as the conclusion of a syllogism, which involves 3 propositions. – user20153 Nov 25 '16 at 22:51
  • Jerry K-- The middle term is the term common to both premises. It connects the two, and enables a conclusion larger than each premise individually. – Mark Andrews Nov 28 '16 at 20:25

It depends on what kind of logic you are studying. In Aristotelean term logic, "all B are C" has existential import, which is to say it is only true if there are B's. Hence it follows by immediate inference that "some B are C". If the point of the exercise is to ask what can you infer from both premises that does not simply follow by immediate inference from either one, then "some A are C" does this but not "some B are C". We would need to see exactly how the question is worded in order to judge whether that is the best answer.

In predicate logic, "all B are C" does not have existential import, which is to say it is trivially true in the event that there are no B's. Hence "some B are C" does not follow from it. To deduce "some B are C" you would need to reason from "some A are B" to "there exists at least one B" and then from this together with "all B are C" to "there exists at least one thing that is B and C".

So for myself, preferring the predicate logic approach, I would say you are correct that both "some B are C" and "some A are C" follow.

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I would reach that problem this way:

Some A are B

All B are C (so, some A are the same as B, this means some A are C )


Some B are C - cannot be the right answer as it is clearly said previously that all B are C

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