## Diagram?

Prepare for the LSAT or discuss it with others in this forum.
shakenbake021

Posts: 7
Joined: Sat Nov 14, 2009 4:40 am

### Diagram?

How do you diagram the following:

If it is not A, then B only if C.

Thanks!

tomwatts

Posts: 1710
Joined: Wed Sep 16, 2009 12:01 am

### Re: Diagram?

~A and B -> C, I would imagine. (Where ~ indicates negation.) Did this phrasing actually come up in a question that I've forgotten?

itsfine

Posts: 229
Joined: Mon Aug 10, 2009 1:07 am

### Re: Diagram?

shakenbake021 wrote:How do you diagram the following:

If it is not A, then B only if C.

Thanks!

(not a -> B ) -> c

r6_philly

Posts: 10731
Joined: Sat Dec 19, 2009 4:32 pm

### Re: Diagram?

!A -> (B -> C) would be more accurate. the two condition is not parelle, first causes the second condition. IF not A, THEN B... because the reverse is: if A is true then the second condition is not necessarily true. You can't write it as a "and", it is causal.

tomwatts

Posts: 1710
Joined: Wed Sep 16, 2009 12:01 am

### Re: Diagram?

r6_philly wrote:!A -> (B -> C) would be more accurate. the two condition is not parelle, first causes the second condition. IF not A, THEN B... because the reverse is: if A is true then the second condition is not necessarily true. You can't write it as a "and", it is causal.

You know, this is what I first wrote down, but then I changed my mind. I'm pretty sure that what I wrote performs identically to this (at least for LSAT purposes), but it's easier to write a contrapositive.

For instance, if we know we have not A, then we don't know whether we've got B or C. But if we know that we have not A and we know that we have B, then we know we have C. That comes out the same either way. On the other hand, if we know that we don't have C, then we know that we either don't have B or we have A (or both). That's pretty simple to get from the conditional that I wrote, but the contrapositive of yours would be...
!(B->C)->A
And frankly, I don't think I want to think about that on the LSAT.

This is just my second inclination, though, and my first inclination was what you wrote. Am I wrong in some way? Is there some reason that you have to write it the way that you did?

shakenbake021

Posts: 7
Joined: Sat Nov 14, 2009 4:40 am

### Re: Diagram?

Thanks, guys! That was very helpful. Wish I had your diagramming skills! And no, this isn't from an actual test (at least not from one I've taken). I just wanted to know.

itsfine

Posts: 229
Joined: Mon Aug 10, 2009 1:07 am

### Re: Diagram?

itsfine wrote:
shakenbake021 wrote:How do you diagram the following:

If it is not A, then B only if C.

Thanks!

this is correct if it means : if it is not A, then it is B, so long as C.

(not a -> B ) -> c

r6_philly

Posts: 10731
Joined: Sat Dec 19, 2009 4:32 pm

### Re: Diagram?

tomwatts wrote:
r6_philly wrote:!A -> (B -> C) would be more accurate. the two condition is not parelle, first causes the second condition. IF not A, THEN B... because the reverse is: if A is true then the second condition is not necessarily true. You can't write it as a "and", it is causal.

You know, this is what I first wrote down, but then I changed my mind. I'm pretty sure that what I wrote performs identically to this (at least for LSAT purposes), but it's easier to write a contrapositive.

For instance, if we know we have not A, then we don't know whether we've got B or C. But if we know that we have not A and we know that we have B, then we know we have C. That comes out the same either way. On the other hand, if we know that we don't have C, then we know that we either don't have B or we have A (or both). That's pretty simple to get from the conditional that I wrote, but the contrapositive of yours would be...
!(B->C)->A
And frankly, I don't think I want to think about that on the LSAT.

This is just my second inclination, though, and my first inclination was what you wrote. Am I wrong in some way? Is there some reason that you have to write it the way that you did?

Actually the reason is I am a programmer and I think I approach it like that because it is easy to read. And also, in my line of work I almost always have to address the ELSE statement. So I would probably have to write a ELSE for if !A (so if A is true) as well as one for ELSE !B (for when B is true). exception handling frequently require me to seperate logical comaprisons rather than grouping them. Maybe thats why my logic doesn't quite work the way I want on the LR sections under test conditions lol Yours is simpler for the test for sure, I think I should probably use more study guides