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): You can put this solution on YOUR website!
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:
\ =\ 20)
\ =\ 7)
\ =\ 2*n(A))
And lastly, from the definition of set union, we can say:
)
From which we can deduce:
\ =\ n(A_o)\ +\ n(B_o)\ +\ n\left(A\small\cap\LARGE B\right))
From the definitions of and we know that
)
and
)
But since
\ =\ 7)
We can say
\ =\ n(A_o)\ +\ n\left(A\small\cap\LARGE B\right)\ =\ n(A_o)\ +\ 7)
and
\ =\ n(B_o)\ +\ n\left(A\small\cap\LARGE B\right)\ =\ n(B_o)\ +\ 7)
Rearranging 9 and 10 we get:
\ =\ n(A)\ -\ 7)
and
\ =\ n(B)\ -\ 7)
Substituting 11 and 12 into 5:
\ -\ 7\ +\ n(B)\ -\ 7\ +\ 7\ =\ 20)
Then a little arithmetic:
\ +\ n(B)\ =\ 27)
Substituting 3 into 14:
\ +\ 2*n(A)\ =\ 27)
Or:
\ =\ 27)
The rest is just arithmetic.
John
My calculator said it, I believe it, that settles it
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