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

Alum Member
188 karma
I thought it was, but I'm second-guessing myself. Can you help me better understand this concept?
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• #### is that if A, then not B, and A or B, but not both the same thing?is that if A, then not B, and A or B, but not both the same thing?

• Live Sage
3107 karma
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.
• Alum Member
188 karma