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Critical Reasoning -- Deductive Reasoning
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Author:  questioner [ Tue Apr 10, 2012 10:16 pm ]
Post subject:  Critical Reasoning -- Deductive Reasoning

In Critical Reasoning -- Deductive Reasoning (http://www.800score.com/content/guidec3IV3.html),
the explanation of rule #5 says that if some A are B then
the below 2 inferences are invalid:

-Some A are not B
-Some B are not A

I am not able to understand the logic behind this. Could
you please explain with some examples? Thanks.

Author:  Nick [ Tue Apr 10, 2012 11:45 pm ]
Post subject:  Re: Critical Reasoning -- Deductive Reasoning

Examples definitely help when thinking through deductive reasoning. So let's make up a fake family called the 'Andersons.' That will be 'A' and let's replace 'B' with 'Banker.'

We are told some Andersons are Bankers. Given this, however, we cannot infer that:

Some Andersons are not Bankers
This is an invalid inference because being told "some Andersons are Bankers" leaves open the possibility that all Andersons are Bankers (maybe everyone in the Anderson family really loves banking). If all Andersons are Bankers then it would not be true that some Andersons are not Bankers.

Some Bankers are not Andersons
This is an invalid inference because being told "some Andersons are Bankers" leaves open the possibility that all Bankers are Andersons (maybe this hypothetical takes place in a strange country where only the Anderson family is allowed to run banks). If all Bankers are Andersons then it would not be true that some Bankers are not Andersons.

Author:  smohit04 [ Wed Apr 11, 2012 9:19 am ]
Post subject:  Re: Critical Reasoning -- Deductive Reasoning

Thanks Nick. But if in the question stem its stated that only some Andersons are bankers, then why should we assume that all Andersons may be bankers... Shouldn't we just accept the given fact as 100% true that only some A are B and not all A MAY BE B...?

Author:  Nick [ Thu Apr 12, 2012 4:12 pm ]
Post subject:  Re: Critical Reasoning -- Deductive Reasoning

We are told "some A are B," we are not told "only some A are B" as you suggest. It's critically important not to assume more than exactly what the text says. "Some" does not mean "only some but not all."

So the statement "some A are B" leaves open the possibilty that all A are B. In my explanation I didn't say all A must be B, only that all A could be B, and thus we cannot infer that some A are not B.

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