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) (Show Source):
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