@Paul80 of course! These drills are asking you to supply the missing premise that would make the conclusion follow logically.
So these drills are effectively Strengthen with Sufficient Premise questions stripped down to the pure formal logic.
Let's take a closer look at this specific drill:
P1: X ==> Z not Z ==> not X
P2: not D ==> not Z Z ==> D
So these are the first two premises with the contrapositives written directly underneath.
What can you properly conclude from these premises?
Using the transitive property, we can conclude: not D ==> not X
This deduction is made using P2 and the contrapositive of P1:
not D ==> not Z ==> not X
Our conclusion in this drill, however, is "not D ==> A" which is not the same as "not D ==> not X."
So what's the missing premise?
We need to connect "not X" to "A" to validly complete this argument.
So the missing premise here is:
not X ==> A not A ==> X
So (E) would be the correct answer.
Here is the final transitive chain and the contrapositive:
not D ==> not Z ==> not X ==> A not A ==> X ==> Z ==> D
Hope that helps! Please watch our video lessons on Sufficient & Necessary Conditions and Strengthen Questions for a more in-depth discussion of these topics.
