Please let us know if you have any other questions.
jorge10rod44September 1, 2018
Could I receive an explanation on how the C was reached? Perhaps a list of rules or guides to follow?
MehranSeptember 2, 2018
Hi @jorge10rod44, thanks for your post.
Let's start with the three given premises: P: A ==> not B the contrapositive is: B ==> not A
P: C ==> X the contrapositve is not X ==> not C
P: not C ==> B the contrapositive is not B ==> C
You can combine the first premise, the contrapositive of the third premise, and the second premise, into one long transitive chain: A ==> not B ==> C ==> X therefore: A ==> X
This is answer choice (C).
You can find detailed lectures helpful to developing these skills in our "Sufficient & Necessary" lecture and in our "Argument Structure" lecture.
Hope this helps!
JCarterSeptember 4, 2018
On the explanation above, why are you combining the first premise , the second premise, and the contrapositive of the third premise? What are you selecting these premises? Why not the contrapositives of the others or the third premise?
Max-YoungquistSeptember 5, 2018
@JCarter we want to try to connect the premises together to make one of the answer choices work as a conclusion. In our case, we have answer choices that start from X, A or not X.
Note we cannot deduce anything from X.
not X we have: not X ==> not C ==> B ==> not A, but that's not an answer choice.
So here we connect them as Mehran details above simply because that's how to get from A ==> X. If one of the answer choices was not X ==> not A, we could have reached that as I just diagrammed.
In general, your strategy should be to connect premises to create the longest transitive chain possible. The longer the chain, the more deductions you can make.
