LSAT Q&A: Ask the Experts Forum

[matt@manhattanlsat]

Can someone show me how to take the contrapositive of the following conditional statement?

Original: If A but not B, then C.

It's from PT 62 (Dec. 2010), LR 1, Question 19.
I choose the wrong answer choice E, and I wonder why is it wrong for me to conclude that: if ~C, then either ~A or B.

The premise you're referencing is that any pet store that sells tropical fish but not exotic birds does sell gerbils.

TF + ~EB --> G

Answer choice (E) also uses the last premise that if the pet store is independently owned, it does not sell gerbils.

IO --> ~G

We can infer:

TF + ~EB --> ~IO

Answer choice (E) can be notated:

IO + ~TF --> EB

This is real close, but it should have stated:

IO + TF --> EB

According to the stimulus, if the store in not independently owned, then either it does not sell tropical fish or it does sell exotic birds. So if it sold tropical fish, we could infer that it sold exotic birds. Or if it did not sell exotic birds, we could infer that it did not sell tropical fish.

[Dave Hall]

Can someone show me how to take the contrapositive of the following conditional statement?

Original: If A but not B, then C.

It's from PT 62 (Dec. 2010), LR 1, Question 19.
I choose the wrong answer choice E, and I wonder why is it wrong for me to conclude that: if ~C, then either ~A or B.

Much thanks!

It sounds to me like you've got the principle down; I suspect you just had trouble with the double negative in (E).

The correct symbolization is as you've indicated:

A + not-B → C
not-C → not-A or B

In the passage in question, we've got:

F + not-B → G
not-G → not-F or B

Since all the independent stores are not-G, we know that every independent is either not-F or else B.

So, every independent store either doesn't carry Fish, or else it does carry Birds; at least one of those conditions is always satisfied.

Thing is, this means that if a store doesn't carry Fish, it has satisfied at least one of the conditions (namely, not-F), and we can't make any conclusion about the Birds.

On the other hand, if an independent store did carry Fish, then it would not have satisfied the necessary not-F condition, and we would then know that it must satisfy the only other possible condition - if it did carry Fish, then it must also carry Birds.

Another way of saying that is this:

What you want (like every other normal human) is for (E) to say "If it doesn't satisfy condition A, then it must satisfy condition B".

The problem with answer choice (E) is in the double negative: If the store doesn't carry Fish, then that means that it has satisified condition A, which means that it doesn't have to also satisfy condition B. If you took out the word "not" in the choice as written, then it would be correctly inferred!

Whew. That was... fun?

Let me know if you need more,

d

[Edit: Oops. I didn't see that Noah had already answered. Didn't mean to be reiterative].

[Systematic1]

This is a stupid question, but can someone explain what it means to "qualify" a statement? I'm guessing it means to substantiate or give evidence in support of, but something online said it is to limit or express reservations. Any help would be appreciated.

[Dave Hall]

This is a stupid question, but can someone explain what it means to "qualify" a statement? I'm guessing it means to substantiate or give evidence in support of, but something online said it is to limit or express reservations. Any help would be appreciated.

Not stupid (every question is easy once you already know the answer; that doesn't mean it's easy before you know).

Anyway, what you read online is true. To qualify does not mean to substantiate; to qualify a statement is to limit it in some way.

So, for example to say, "I'd recommend doing blow without qualification" is to say that you fully recommend the yayo, without any reservations.

Or, "Yeah, I'm pretty sure your entire plumbing system will need to be removed and replaced. Of course, I should qualify that by saying that I'm not a plumber (but I did leave an upper-decker in your guest bathroom)." This means that the speaker is limiting his advice by referencing his ignorance (and also, that he's pretty much a douche).