Contrapositives question--ANSWERED, thank you!! Forum

[chrisnlis]

I'm on pg. 81 of "Cracking LSAT-2012 edition" where it gives the following:

If Pablo attends the dance, Christina won't attend the dance.

P --> ~C

However, it gives the contrapositive as

C --> ~P

To me this makes no sense. In the original, Christina based her decision upon Pablo's actions.
So, can someone explain why the contrapositive is not

~P --> C

This to me keeps with the original statement, that Christina's actions hinge upon Pablo's, not the other way around.


Thanks! This is the first book I'm using, then LGBible, then Atlas. Kaplan 180 & Kaplan LG if I have time. So far not having much issue with LR, but if I do, maybe LRBible?

If anyone has any helpful critique of my chosen study materials, please advise. I mostly went with what got high ratings on Amazon (which is why I avoided Princeton's LG Workout).

[gchatbrah]

The first thing to keep straight is the formality here. By definition, if you have:

P --> ~C

then the contrapositive must be C ---> ~P. A contrapositive (1) inverts the original statement and then (2) negates both sides. That's what we've done here to get from P ---> ~C to C ---> ~P.

That's a logical structure you just need to lock down in your mind. That's the formulaic way to get to the correct answer.

Now, as a practical matter, think about your suggestion of ~P ---> C being the contrapositive. As a logical matter, the contrapositive of a true statement MUST be true. Is that the case here? Not necessarily. All we know from the original statement is that if Pablo attends, C is absolutely not attending. That doesn't mean that if P decides to stay home, C will decide to attend. It's just as likely that C is not going to attend the dance at all, regardless of whether P goes or not.

Since the statement you propose -- ~P --> C -- is not necessarily true, it CANNOT be a contrapositive, which is a statement that is always true.

[kartelite]

I'm on pg. 81 of "Cracking LSAT-2012 edition" where it gives the following:

If Pablo attends the dance, Christina won't attend the dance.

P --> ~C

However, it gives the contrapositive as

C --> ~P

To me this makes no sense. In the original, Christina based her decision upon Pablo's actions.
So, can someone explain why the contrapositive is not

~P --> C

This to me keeps with the original statement, that Christina's actions hinge upon Pablo's, not the other way around.


Thanks! This is the first book I'm using, then LGBible, then Atlas. Kaplan 180 & Kaplan LG if I have time. So far not having much issue with LR, but if I do, maybe LRBible?

If anyone has any helpful critique of my chosen study materials, please advise. I mostly went with what got high ratings on Amazon (which is why I avoided Princeton's LG Workout).

Logic is not about people making decisions, it is about describing a state of the world.

If Pablo attends the dance, then Christina won't attend the dance. We are told this. This is a true fact about the world. If Pablo is at the dance, then Christina won't be there. That means they can't both be at the dance.

What if Christina is at the dance? Can Pablo be there? Well, a fact is that if Pablo is at the dance, then Christina isn't. Can Christina both be at the dance and not be at the dance? No. So obviously if Christina is at the dance, then Pablo cannot be at the dance. C --> ~P

[transferror]

I'm on pg. 81 of "Cracking LSAT-2012 edition" where it gives the following:

If Pablo attends the dance, Christina won't attend the dance.

P --> ~C

However, it gives the contrapositive as

C --> ~P

To me this makes no sense. In the original, Christina based her decision upon Pablo's actions.
So, can someone explain why the contrapositive is not

~P --> C

This to me keeps with the original statement, that Christina's actions hinge upon Pablo's, not the other way around.


Thanks! This is the first book I'm using, then LGBible, then Atlas. Kaplan 180 & Kaplan LG if I have time. So far not having much issue with LR, but if I do, maybe LRBible?

If anyone has any helpful critique of my chosen study materials, please advise. I mostly went with what got high ratings on Amazon (which is why I avoided Princeton's LG Workout).

Logic is not about people making decisions, it is about describing a state of the world.

If Pablo attends the dance, then Christina won't attend the dance. We are told this. This is a true fact about the world. If Pablo is at the dance, then Christina won't be there. That means they can't both be at the dance.

What if Christina is at the dance? Can Pablo be there? Well, a fact is that if Pablo is at the dance, then Christina isn't. Can Christina both be at the dance and not be at the dance? No. So obviously if Christina is at the dance, then Pablo cannot be at the dance. C --> ~P

Scoop. +1

[transferror]

Also, http://en.wikipedia.org/wiki/Contraposition

[chrisnlis]

Thank you both for the VERY CLEAR answer...it makes perfect sense now!

That is the only type of LR that has had me confused. I totally didn't get from the first example they gave (before this one) that switching the order was part of the formula. I see now, that they mentioned it, but it wasn't one of those *bullet points* that they use everywhere else to make you take notice.


THANK YOU!!!

[transferror]

Also, don't do Kaplan. The point of a rigorous course like Kaplan is to first tear down your pre-conceptions about how things work and then "rebuild" you in their system. I know many who have had their scores decrease in the first 6-8 weeks of Kaplan LG for this reason. The idea is that after that, your scores will rise exponentially as you understand/become efficient with their system. If you use other systems/methods first, forget about Kaplan. It's no good unless you have a lot of time and are willing to shed most of your prior knowledge. Based on what some of my peers did, it's best to find one system and stick to it. 6-8 months of the Bible (or whatever else) > 2 months of each system.

[Clearly]

Take that book, find the nearest dumpster, and carefully, using gloves to protect you from it, place it in.