Formal Logic Question

sottovoce
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Joined: Tue Nov 13, 2012 8:43 am

Formal Logic Question

Postby sottovoce » Thu Jan 01, 2015 9:50 pm

Hey guys,

This might be a really basic question and I feel dumb here. But on one of the questions in the Logic Reasoning Bible it asks you to give inferences and diagrams of certain premises.

So it says:
Some T's are U's.
All U's are V's.
All T's are S's.

Final diagram I got right:
S <--- T some U --> V

However, one of the inferences is S some V!

I thought that is not necessarily true.

Let's say that there are two components of T, half which are made out of S (some S's are T's) and half of which are NOT made out of S. We know that some T's are U's. But let's say that the T's that ARE U's are composed only of the half that is not S's! This would mean, even though all U's are V's, there is no connection between U and S, and in this situation exactly 0 S's are V's.

I am probably have a flaw in my logic. Please let me know. Thanks.

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RZ5646
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Re: Formal Logic Question

Postby RZ5646 » Thu Jan 01, 2015 9:59 pm

What is powerscore's inference? Some V's are S's? Or some S's are V's?

sottovoce
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Joined: Tue Nov 13, 2012 8:43 am

Re: Formal Logic Question

Postby sottovoce » Thu Jan 01, 2015 10:07 pm

Some S's are V's. S some V.

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CardozoLaw09
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Re: Formal Logic Question

Postby CardozoLaw09 » Thu Jan 01, 2015 10:15 pm

Final diagram I got right:
S <--- T some U --> V



At least one V is a U, and at least one U is a T, and all T's are S's, so there could be one V that's also an S aka V some S or S some V

sottovoce
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Joined: Tue Nov 13, 2012 8:43 am

Re: Formal Logic Question

Postby sottovoce » Thu Jan 01, 2015 10:22 pm

CardozoLaw09 wrote:
Final diagram I got right:
S <--- T some U --> V



At least one V is a U, and at least one U is a T, and all T's are S's, so there could be one V that's also an S aka V some S or S some V


Thanks so much. I am trying to get it in a little bit more conceptual terms. Can you explain to me why my scenario doesn't make sense?

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RZ5646
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Re: Formal Logic Question

Postby RZ5646 » Thu Jan 01, 2015 10:24 pm

Ok you made a mistake right at the beginning: "Let's say that there are two components of T, half which are made out of S (some S's are T's) and half of which are NOT made out of S."

That contradicts "All T's are S's." You can't have a T that is a non-S, since we're told that every T is an S.

Basically since every T is also an S, you can just substitute S for T (though not the other way around). Same thing with U and V. So when you read "some T is U," you can make that "some S is V."

You can also look at it with Venn diagrams
Image

or just regular non-powerscore formal logic
Image

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NL2424
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Re: Formal Logic Question

Postby NL2424 » Fri Jan 02, 2015 1:13 am

..
Last edited by NL2424 on Fri Jul 10, 2015 10:22 pm, edited 1 time in total.

Rook
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Re: Formal Logic Question

Postby Rook » Tue Jan 06, 2015 2:22 pm

my inferences are: some t's are v's, some u's are s's, some v's are s's...

are these correct?




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