Let's take a close look at the premises and think about how they might be linked up into transitive arguments.
P1: B - > not C
CP1: C - > not B
P2: not A - > C
CP2: not C - > A
P3: A - > Z
CP3: not Z - > not A
Now, combine CP3 with P2 and CP1, as follows:
not Z - > not A - > C - > not B
is equal to not Z - > not B, which is answer choice (A).
You've flipped the sufficient and necessary conditions. Remember: you can't just reverse.
Hope this helps! And good luck tomorrow!
dekker0711September 22, 2017
These problems don't seem to make any sense to me at all
Chakera-HightowerOctober 15, 2019
How do I know to choose the notZ ==> notB answer over B ==> Z conclusion?
SabrinamcJuly 10, 2020
I have the same question as Chakera Hightower. I find myself concluding to B-->Z instead of not Z-->not B
SabrinamcJuly 10, 2020
I only selected the correct answer bc my conclusion was not an option.
VictoriaJuly 16, 2020
Hi @Chakera-Hightower and @Sabrinamc,
Thanks for your questions. Hopefully I can help clear things up a bit!
Both B --> Z and Not Z --> Not B are valid conclusions drawn from the premises. For this particular example, the reason that you would select not Z --> not B is because it is the only valid answer choice.
These missing premise/conclusion drills are intended to get you to practice specific skills. This example is focused on drawing conclusions from the contrapositive.
The important thing is that both conclusions are valid, but the contrapositive is the only one represented in the answer choices and that is why (A) is the correct answer.
Hope this is helpful! Please let us know if you have any further questions.
ForestJune 9, 2022
Hello Victoria, thank you and Mehran for your responses. Would it be possible to explain why we are looking for a contrapositive answer instead of a positive one?
Emil-KunkinJune 10, 2022
Hi,
We are not looking for only a contrapositive or a positive answer choice- either would be correct. Since a statement and its contrapositive express the same idea, and answer choice would be correct regardless of wether it is the original statement or its contrapositive. In this case, the answer was phrased as the contrapositive, but it could equally have been phrased as the original statement.
