double not arrow question

[lsattaker]

#1.
A --------> B <------|------> C, we all know = A<------|------> C, but what about ~A --------> B <------|------> C, does this = ~A<------|------> C? or does it = something else? Please explain. Thanks.

#2.
~A------>B
CONTRAPOSTIVE = ~B------>A

~B------>C

Can I link them to be A------>~B------>C? Please explain. Thanks.

#3.
Also, what about this A------>~B------>C? Does = A------>C or A------>~C? Please explain. Thanks.

[Dave Killoran]

Hi lsattaker,

Let's look at each of the three questions you posted:

1. You ask about this relationship: A B C. Let's break that into component parts:

• A B
  
  B C

Viewed from that angle, it's easier to see that this is really:

• A B C

Thus, the inference is that:

• A C

Since both terms are negative, I'd take the contrapositive, which is:

• C A

2. No, you can't link them like that unfortunately. The contrapositive was B A, but in linking them you performed a Mistaken Reversal and turned it into A B. That arrow should actually be reversed, which would result in:

• A <--- B ---> C

The inference there is that "Some As are Cs." While that inference is useful in LR, in LG it has never been used to produce a correct answer and thus we don't pay much attention to it.


3. It's A C. The B is just a weigh station of sorts that you skip right over. It doesn't matter if B is negative or not; the status of B doesn't affect A and C.


It's interesting, there's a chapter on Formal Logic in the LRB that you should read, if you have that book. I think it would help all of this make even more sense. Formal Logic encompasses conditional reasoning and then adds terms like "some" and "most," creating a whole new set of inferences. I often tell students that they don't need to master Formal Logic to do well on the LSAT, but if they do, it automatically makes them conditional reasoning masters.

Please let me know if that above helps. Thanks!