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Formal Logic Question
Posted: Thu Jul 19, 2012 4:09 pm
by JMCSpartan08
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.
Re: Formal Logic Question
Posted: Thu Jul 19, 2012 4:26 pm
by Malapropism
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
Re: Formal Logic Question
Posted: Thu Jul 19, 2012 4:30 pm
by poppy
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
Re: Formal Logic Question
Posted: Thu Jul 19, 2012 8:50 pm
by boblawlob
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)
Re: Formal Logic Question
Posted: Fri Jul 20, 2012 4:39 pm
by bp shinners
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.