SOLUTION: Suppose About are sets, AUB has 20 elements, AnB has 7 elements & the number of elements of B is twice that of A ,what's the number of elements in A & B

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Question 934864: Suppose About are sets, AUB has 20 elements, AnB has 7 elements & the number of elements of B is twice that of A ,what's the number of elements in A & B
Answer by solver91311(24713) About Me  (Show Source):
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In that set is non-empty, there exists a set that we will denote whose elements are those elements of set that are NOT contained in set . Likewise, is the set of elements of set that are not contained in set . For this discussion the notation means "the number of elements in set ".

We are given the following facts:







And lastly, from the definition of set union, we can say:



From which we can deduce:



From the definitions of and we know that



and



But since



We can say



and



Rearranging 9 and 10 we get:



and



Substituting 11 and 12 into 5:



Then a little arithmetic:



Substituting 3 into 14:



Or:



The rest is just arithmetic.

John

My calculator said it, I believe it, that settles it