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Skylar on March 30, 2020

@cholman, happy to help!

Let's start with the Missing Premise Drills. In this lesson, the drills are meant to familiarize you with the Sufficient & Necessary logic used in LSAT without all of the confusing language.

The Missing Premise Drills present 1-2 given premises, 1 missing premise, and 1 conclusion. You are tasked with coming up with the missing premise that will fill in the missing link and connect all of the pieces together. You should start by finding the contrapositives of all the given premises/conclusions, and then identify the two variables you must connect for the chain to be fully connected together and the conclusion to be properly drawn. The statement in which you connect these two variables and the contrapositive of this statement are your correct answers. You can check this by making sure that this statement can be combined with the other premises to result in the conclusion. The correct answer will also be listed for you on the back of the notecard.

Here's an example of how to work through a Missing Premise Drill:
P: A -> B
P: ?
C: not B -> C

The first step you should take is to find the contrapositive of the statements you were given. To do this, you should reverse and negate. This gives us:
P: A -> B
not B -> not A
P: ?
C: not B -> C
not C -> B

Now, you should look for a way to connect the premise to the conclusion. You may find two routes (depending on whether you start from the original statement or the contrapositive). Either one is valid. In fact, one will be the contrapositive of the other.

Route 1: We know we want to be able to conclude that "not B -> C." However, we don't have anything about C mentioned in our premises currently. So, we should note that we need to incorporate the new variable C with something related to "not B." The contrapositive of our first premise tells us that "not B -> not A" so we should use "not A" as the related variable we want to connect to C. We can therefore answer: "not A -> C." This works as the missing premise because it allows us to use the transitive property to connect: not B -> not A -> C. This ultimately fills the gap and allows us to conclude that not B -> C.

Route 2: We could also connect the original first premise (A -> B) to the contrapositive of the conclusion (not C -> B). Again, we know that we need to introduce the new variable "not C" and we know that we need to make it related to "B." We can therefore say: "not C -> A." This allows us to use the transitive property on "not C -> A -> B" to ultimately conclude that "not C -> B."

Does this make sense? I will follow up shortly with a breakdown of an Argument Completion drill.

Skylar on March 31, 2020

@Crook, now let's look at an Argument Completion drill.

We can approach these drills in the same way that we approached the Missing Premise Drills. In fact, some of the Argument Completion Drills follow the exact pattern we worked through in our Missing Premise Drill above. In these, the key idea is to complete the argument logically.

Let's work through a new Argument Completion Drill:
P: X -> C
P: not X -> A
P: ?
C: not A -> Z

We should start by finding the contrapositives of the statements we've 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, we need to create a third premise that will connect the previous two premises to the conclusion. We notice that the new variable introduced in the conclusion is Z, so we should start there.

According to the conclusion about Z, we want to connect it from "not A." Where else do we see "not A" in our other statements? We see it in the contrapositive of our second premise, which states "not A -> X." Where else do we see X in our other statements? We see it in our first premise, which states "X -> C." Therefore, we can follow this chain through all the way down to C, which we want to connect to Z.

This gives us a chain of: not A -> X -> C -> Z.
We simplify this to get the conclusion: not A -> Z.
The piece that we added was: C -> Z, so this is our missing premise.
The contrapositive of this missing premise is: not Z -> not C.
This gives us:
P: X -> C
not C -> not X
P: not X -> A
not A -> X
P: C -> Z
not Z -> not C
C: not A -> Z
not Z -> A

We could have also approached this starting from the contrapositive of the conclusion. This would give us the chain: not Z -> not C -> not X -> A.

Does that help? Please let us know if you have any other questions and best of luck with your studies!

cholman on April 13, 2020

hi, i've been going through the missing premise drills and i definitely have a better understanding so thank you!

i was wondering though, on the card that says
P: X -> A
P: ?
C: not A -> B
should the missing premise be not X -> B? the card says that is the contrapositive of the missing premise but i don't understand how. thanks!

cholman on April 13, 2020

i was also wondering, on the card that says
P: X -> C
P: not X -> A
P: ?
C: not A -> Z
the answer is C -> Z, but I was wondering why it couldn't be A -> Z?