Is {A some /B} equal to {/A some B} ?

S.P. 170

I thought it was, but I'm second-guessing myself. Can you help me better understand this concept?

Accounts Playable

No, they are not.

Say we have this set of things:

A/B
A/B
A/B

/AB


Some As are not Bs (3 As are in fact not Bs). Some not As are Bs (one not A is a . Those two sets are different since their elements are different. For two sets to be equal, the elements in both sets and only those elements have to make up the entirety of both sets.

Intuitively, think of this example:
Some dogs are not cats. Some not dogs are cats. These two sets are not the not same because we can intuitively see that some dogs aren't cats (since all dogs are not cats). But, something that is not a dog (i.e. a cat) is a cat is also intuitively true. Thus, these two sets are not equivalent because they don't have the same meaning.

S.P. 170

Great answer. Thank you.

quinnxzhang

Here's a clearer example:

"Some YLS students have not taken the LSAT" is false. "Some people who are not YLS students have taken the LSAT" is true. This shows that "some A's are not B" is not equivalent to "some not A's are B".

MrSamIam

Nope, they're two completely different statements.

The first reads, "Some As are not Bs": So, if we have 10 As, at least one of them is not a B.

The second reads, "Some things that are not As, are Bs": There's more flexibility with this statement. What isn't an A? Tons of things! So maybe we have some Hs, Ks, and Zs...and some of those are Bs. But, none of the As are Bs...or maybe all of the As are Bs.