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

Mehran October 4, 2016

@Angie12 let's take a closer look.

P: X-some-Y
Y-some-X

P: ?

C: Z-some-Y
Y-some-Z

Notice the jump in this argument. We are given nothing related to Z in our premise.

We only know Y-some-X so we need to incorporate Z to properly arrive at the conclusion Y-some-Z.

This means we need X to be sufficient for Z as follows:

Y-some-X ==> Z

So our missing premise is:

X ==> Z
not Z ==> not X

This allows us to properly conclude: Y-some-Z

Hope that helps! For a more in-depth discussion of these concepts, please watch our video lesson on Quantifiers.

Ceci August 19, 2018

These are usually the ones I guess on and thankfully I get them right sometime but I have NO idea what I'm doing or how it follows logically

smatsunaga May 3, 2021

This is confusing because the conclusion is Z-some-Y

Victoria May 23, 2021

Hi @smatsunaga,

Remember that 'some' statements are reversible!

Hope this helps! Please let us know if you have any further questions.

Krystina January 20, 2022

How do did we decide that x is the sufficient? What gives us this clue?

Ravi February 4, 2022

@Krystina, X is not the sufficient condition here since it's a "some" statement. Some statements are reversible, so there is no sufficient or necessary condition with them.