P: Y → Z & not AP: B → AP: C → BP: Z and B exist.C: ?

CJFisch September 6, 2016

"Z exists"

Hello. I'm having difficulty understanding the function of, "Z exists," in regards to the answer choice. I thought that since the premise, "Z and B exist," that would mean that both must be factored into the answer, which would have lead to the "No Valid Conclusion," answer because it would have been both, "A exists," and, "A does not exist," Y - > Z and not A B - > A Would it be possible to give a more thorough explanation? I would appreciate it. Thank you for your time

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Mehran September 7, 2016

@CJFisch let's break this drill down.

First things first, let's write out the contrapositive for each principle.

P: Y ==> Z & not A
not Z or A ==> not Y

P: B ==> A
not A ==> not B

P: C ==> B
not B ==> not C

Okay, we are then told that Z and B exist.

Notice that having Z tells us nothing because Z is necessary in our first premise (don't just reverse!).

Having B, on the other hand, allows us to conclude that A exists (from the second premise).

Now, from the existence of A, we are able to conclude that Y does not exist (from the contrapostive of the first premise).

As such, (D) is the correct answer here, i.e. A exists and Y does not.

Hope this helps! For a more detailed discussion of these concepts, please watch our video lesson on Sufficient & Necessary conditions.

CJFisch September 8, 2016

Thank you for the explanation/clarification!