Supply the missing premise that makes the conclusion follow logically:P: X–some–YP: ?C: Z–some–Y

bcross May 29, 2020

Why couldn’t the second answer be true?

I am having a lot of trouble understanding what’s going on in this problem? I think it’s because I’m unclear of that “some” means in this context. I read the other posts and am still confused. Additionally, could you explain why B is not correct?

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BenMingov May 31, 2020

Hi Bcross, thanks for the question.

The easiest method to approach these drills is to take apart the conclusion and use information given to determine the missing piece.

The conclusion here is Z -some- Y

Take it apart and you are left with:

Z Y

Now fill in what is given.

Z X -some- Y

The missing link is going from X to Z. If X then Z (X -> Z and its contrapositive Not Z -> Not X)

This creates:

Z <- X -some- Y

Which in the end gives us Z-some-Y.

Using B, we would fill in the link this way.

Z X -some- Y

Becomes (using the contrapositive of B, Z -> X)

Z -> X -some- Y

Which is not Z-some-Y. Our deduction needs to start from the some and move towards the all arrow. Not the other way around.

Please let me know if this is clear. If not, I'd be happy to elaborate!