## Formal Logic Question

Prepare for the LSAT or discuss it with others in this forum.
JMCSpartan08

Posts: 37
Joined: Mon Jul 18, 2011 1:36 pm

### Formal Logic Question

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

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

poppy

Posts: 7
Joined: Wed Jul 18, 2012 2:20 am

### Re: Formal Logic Question

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

boblawlob

Posts: 519
Joined: Mon Oct 11, 2010 7:29 pm

### Re: Formal Logic Question

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: 3086
Joined: Wed Mar 16, 2011 7:05 pm

### Re: Formal Logic Question

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.