Supply the missing premise that makes the conclusion follow logically: P: D–most–BP: ?C:B–some–C

Ravi January 2, 2019

@Gianna-Rossi,

Happy to help. We're asked to supply the missing premise that makes
the conclusion follow logically.

We're given P: D-most-B

This can be re-written as B-some-D. We have both options to use
depending on which makes it easier for us to see the link and how it
can connect with another premise to support the conclusion.

We're then given the conclusion: B-some-C. This can also be written as C-some-B.

P: D-most-B (which is B-some-D)

C: B-some-C (which is C-some-B)

If we add D - >C to B-some-D, we get

B-some-D - ->C

If some Bs are Ds, and if all Ds are Cs, then some Bs must be Cs (B-some-C)

The missing premise, therefore, is D - ->C, which is answer C.

In these questions, it helps to solve the missing premise so that once
we look at the answer choices, we already know exactly what we need to
look for.

The key to solving this problem is knowing that D-most-B can also be
written as B-some-D.

B-some-D allows us to see much more easily the relationship between it
and the conclusion of B-some-C.

Does this make sense? Let us know if you have any more questions—we're
here to help!

mg123 August 22, 2019

Why can we assume the D-most-B can also be written as B-some-D? Couldn't you also write that B-most-D?

Irina August 22, 2019

No, the proper inference from Most As are Bs is Some Bs are As. Consider an example:

Most CEOs are wealthy.

We can infer that at least:

Some wealthy people are CEOs.

But we cannot conclude that:

Most wealthy people are CEOs

as it is entirely plausible that most wealthy people hold other jobs.

Does this make sense?

JerryYu October 23, 2019

Thank you Irina! Your example makes perfect sense.