@LSATChris Great question. These drills are designed to give you practice in determining contrapositives and identifying missing premises that are necessary for a conclusion to be logically drawn in an argument. This is a skill that is often tested on the LSAT, as missing premises can create a flaw in reasoning. Essentially, you can think of real LSAT questions as word problems for which these drills are simplified variable problems. They remove the words that students often find overwhelming at first in order to more clearly show the breakdown of the argument. The more you familiarize yourself with these drills and with real LSAT questions, the clearer this connection will become.
In this question, we are given two premises and a conclusion. We are asked to identify the missing premise that will connect the other two premises to the conclusion.
We should start by first determining the contrapositives of all the given statements.
P: D -> A not A -> not D P: C -> D not D -> not C C: not X -> A not A -> X
Next, let's evaluate where the disconnect occurs.
We see that the first two premises can be combined using the transitive property to make: C -> D -> A Combining the contrapositives also gives us: not A -> not D -> not C
The conclusion is making a connection between the variable "A" and a new variable- "X" (in this case, "not X.") So we know that we need to connect "not X" to the chain in a way that will end in it leading to "A." In order to do this, we can add "not X" to the first chain we constructed, which ended with the variable A. This would result in: not X -> C -> D -> A
The same procedure can be done with the contrapositive instead. We know that we need to connect "not A" to "X" according to the contrapositive of the conclusion, so we can add "X" to the end of the contrapositive chain we constructed to get: not A -> not D -> not C -> X
The most direct link between this new variable (X/not X) and the chains we constructed is "not X -> C" in the first case, and "not C -> X" in the second case. Therefore, one of these will be the missing premise, which is what the question is looking for. Note that the one not given as an answer choice is simply the contrapositive of the missing premise (to which it is identical in meaning). Often, the LSAT will test the contrapositive because it is an extra step for students. Here, we see "not X -> C" is the only one of the two direct links given as a choice, so (A) is correct.
Does this help to explain how the map flows? Please let us know if you would like any further explanation!
