Not all As are Bs.All As are Cs.What can you properly infer?

megmcdermott October 5, 2019

Help

Could someone please explain how the conclusion was deduced? I tried to understand from the automatic explanation provided but am still confused. Thank you!

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Skylar October 5, 2019

@megmcdermott Happy to help! Let's take a look.

We are told "Not all As are Bs." This has the same meaning as "some As are not Bs" which can be diagrammed as:

A - some - not B
not B - some - A

The second given statement reads "All As are Cs." This is diagrammed as:

A -> C
not C -> not A

Since we have a quantifier that shares the Sufficient condition with a some statement, we can go ahead and make a valid deduction.

C - some - not B
not B - some - C

This is verbally stated as "some Cs are not Bs," which means that "not all Cs are Bs."

Does this make sense? Please reach out with any additional questions!