Formal Logic Question Forum

[sottovoce]

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.

[RZ5646]

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

[sottovoce]

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

[CardozoLaw09]

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]

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?

[RZ5646]

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


or just regular non-powerscore formal logic

[NL2424]

..

[Rook]

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

are these correct?