June 2010 LSAT Section 5 Question 14

# The author uses the word "immediacy" (line 39) most likely in order to express

Reply

Skylar on April 15, 2020

@cholman, happy to help! I'm glad the drills are becoming clearer for you.Let's take a look at the first card you asked about:

P: X -> A

P: ?

C: not A -> B

Let's find the contrapositives first:

P: X -> A

not A -> not X

P: ?

C: not A -> B

not B -> A

Now, we have two ways to find the missing premise:

(#1) Let's start at the original conclusion: not A -> B. Where else do we see the Sufficient variable of this conclusion, "not A"? We see "not A" in the contrapositive of our first premise, which tells us: not A -> not X. The conclusion that we are trying to reach ends in "B," so we should make our missing premise: not X -> B. This allows us to put together our larger chain of: not A -> not X -> B, which can be simplified into: not A -> B, our conclusion. So, our missing premise is: not X -> B and the contrapositive is: not B -> X.

(#2) We can also start at the contrapositive of our conclusion: not B -> A. Where else do we see the Sufficient condition, "not B"? We don't, so let's look at the Necessary condition, "A." We see "A" in our first premise, which says: X -> A. We know that we want our conclusion to be: not B -> A, so we should make our missing premise: not B -> X. This allows us to make a larger chain of: not B -> X -> A, which can be simplified into: not B -> A. So, our missing premise is: not B -> X and the contrapositive is: not X -> B.

Both "not B -> X" and "not X -> B" are equally valid answers. Either one could be listed as the missing premise, and the other should be listed as its contrapositive.

Let's take a look at the second card you asked about:

P: X -> C

P: not X -> A

P: ?

C: not A -> Z

Again, we should first find the contrapositives of each statement we have been given:

P: X -> C

not C -> not X

P: not X -> A

not A -> X

P: ?

C: not A -> Z

not Z -> A

Now, let's take a look at our conclusion: not A -> Z. Where do we see "not A"? Well, the contrapositive of our second premise tells us that: not A -> X. Where do we see "X"? Our first premise tells us that: X -> C. Where else do we see "C"? We don't. We know that we want our conclusion to end in "Z," so we should make our missing premise: C -> Z. This allows us to make the chain: not A -> X -> C -> Z. This can be simplified into our conclusion, not A -> Z. So, our missing premise is: C -> Z and its contrapositive is: not Z -> not C.

You ask why the missing premise can't be "A -> Z." This is not the correct answer because it does not complete the chain above. Moreover, the contrapositive of "A -> Z" is "not Z -> not A." The contrapositive of the original conclusion we were given is "not Z -> A." We cannot have "not Z" indicating both "not A" and "A."

Does that make sense? Please let us know if you have any other questions and best of luck studying!