Formal Logic Question

JMCSpartan08
Posts: 35
Joined: Mon Jul 18, 2011 1:36 pm

Formal Logic Question

Postby JMCSpartan08 » Thu Jul 19, 2012 4:09 pm

Can you combine two "All" conditionals, to get a valid conclusion, that look like this:

A->C
B->C
----
A->B

OR

A->B
A->C
----
B->C


My gut tells me "no" but I wanted to double check.

Malapropism
Posts: 23
Joined: Mon Jul 16, 2012 8:41 pm

Re: Formal Logic Question

Postby Malapropism » Thu Jul 19, 2012 4:26 pm

Nope. You can only combine like

A-->B
B-->C

to A-->C

Think of it like this:
For the first example, if A is cats, and B is dogs, and C is are animals, all cats are animals, all dogs are animals, but all cats are not dogs.

For the second, if A is cats, B is are animals, and C is have teeth, all cats are animals, all cats have claws, but all animals don't have claws.

I hope that clears things up :)

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poppy
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Re: Formal Logic Question

Postby poppy » Thu Jul 19, 2012 4:30 pm

In the first one you get:

A----> C <-----B

from this you can't infer anything because in order to connect all the variables you'd have to change it to be:

A <-----> C <------> B the double arrow meaning some, and with two some double arrows you can't make an inference

On the second one you get:

B <----- A ------> C

This one you can do B <------> A ------> C or B<------- A <--------> C Both mean the same thing. And from one Some arrow and an All arrow pointing away from the Some arrow you can make inferences.

From this you can infer B <--------> C some B's are C's

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boblawlob
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Re: Formal Logic Question

Postby boblawlob » Thu Jul 19, 2012 8:50 pm

poppy wrote:In the first one you get:

A----> C <-----B

from this you can't infer anything because in order to connect all the variables you'd have to change it to be:

A <-----> C <------> B the double arrow meaning some, and with two some double arrows you can't make an inference

On the second one you get:

B <----- A ------> C

This one you can do B <------> A ------> C or B<------- A <--------> C Both mean the same thing. And from one Some arrow and an All arrow pointing away from the Some arrow you can make inferences.

From this you can infer B <--------> C some B's are C's


Can't you infer from the first statement that some not As are not Bs?

A->C (not C -> not A)
B->C (not C -> not B)

bp shinners
Posts: 3091
Joined: Wed Mar 16, 2011 7:05 pm

Re: Formal Logic Question

Postby bp shinners » Fri Jul 20, 2012 4:39 pm

boblawlob wrote:
Can't you infer from the first statement that some not As are not Bs?

A->C (not C -> not A)
B->C (not C -> not B)


Yes, but you're never going to have to on the LSAT.




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