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Skylar on July 27, 2020

Happy to help!

The Missing Premise Drills are designed to familiarize you with the pattern of logic discussed in this lesson. You can think of LSAT exam questions as word problems to which these drills are simplified versions. We have removed the words that students often find confusing and boiled it down to the basics- just the variables.

Your goal in the Missing Premise Drills is to connect everything you are given in order to make a new deduction about what is missing. First you should identify contrapositives and then you should proceed to look to connect variables.

I'll walkthrough the first drill to show you what I mean by this.

The first drill gives us:
P1: Y -> not A
P2: ?
C: Y -> B

Let's start by finding the contrapositives of the statements we are given,
P1: Y -> not A. The contrapositive of this is A -> not Y.
C: Y -> B. The contrapositive of this is not B -> not Y.

We now have:
P1: Y -> not A
A -> not Y
P2: ?
C: Y -> B
not B -> not Y

So, we need to find a way to connect P1 to C. We see that both P1 and C have an S->N statement where Y is the S condition. Also, C introduces the new variable B, so we'll want to incorporate this in our missing premise. Therefore, we can connect the two original N conditions to say: not A -> B.
P1: Y -> not A
P2: not A -> B
C: Y -> not A -> B
Y -> B

We can also approach this from the contrapositive instead, if that comes more naturally to you. Here, we notice that the contrapositive of P1 and the contrapositive of C are both S->N statements where not Y is the N condition. Not B is a new variable introduced in C that we should look to incorporate in our missing premise. Therefore, we can look to connect the two original S conditions to say: not B -> A.
P1 contrapositive: A -> not Y
P2: not B -> A
C contrapositive: not B -> A -> not Y
not B -> not Y

So, the correct answer for missing P2 is:
not A -> B
not B -> A

Notice that these two statements are the contrapositive of each other. Since contrapositives have the same meaning, it does not matter which you put first as your answer as long as you have both.

I'll walk through another drill:

P: A -> C
P: ?
C: not C -> D

Our first step should be to find the contrapositives of the statements we were given. To do this, we need to reverse and negate.
P: A -> C
not C -> not A
P: ?
C: not C -> D
not D -> C

Now, we should notice that there is a new variable introduced in the conclusion- D. This tells us that we should incorporate it somehow into our missing premise. And what are we told that we want to be able to conclude about D? That not C -> D. Do we know anything about not C? Yes, the contrapositive of our first premise tells us not C -> not A. Therefore, we should make our missing premise not A -> D. This allows us to make the chain: not C -> not A -> D. This simplifies into the conclusion we want, not C -> D. Therefore, our final answer should look like:
P: A -> C
not C -> not A
P: not A -> D
not D -> A
C: not C -> D
not D -> C

If you are still struggling to grasp this concept, I'd suggest looking through this Message Board on the Sufficient & Necessary video as a variety of walkthroughs have been posted in the past.

Does that make sense? Please let us know if you have any other questions!

pmornelasperez@ucdavis.edu on July 29, 2020

Thank you !