SOLUTION: In the venn diagram E is the set of all children in a certain chosen group, A={children in Youth Club A} and B={children in Youth club B}The letters p,q,x and y in the diagram repr

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Question 1023326: In the venn diagram E is the set of all children in a certain chosen group, A={children in Youth Club A} and B={children in Youth club B}The letters p,q,x and y in the diagram represent the number of children in each subset.Given that n(E)=200, n(A)=75 and n(B)=35
(i)find the smallest possible value of y where y is (AUB)'
(ii)the largest possible value of x where x is AnB.
(iii) find the value of of q if p= 45
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

N(A) = 75 = p+x
N(B) = 35 = x+q
n(E) = 200 = p+x+q+y

(i)find the smallest possible value of y where y is (AUB)' 
That'll be when there's the most possible in the two circles,
which is when their intersection x is the least, or when 
x=0, p=75, q=35, and y=90 (that's also when p and q are the
most they can be, and x is the least it can be.)

(ii)the largest possible value of x where x is AnB. 
That'll be when all of B is in x which is when q=0, 
x=35, p=40, and y=125.  (That's also when y is the most
it can be, and when p and q are the least they can be)

(iii) find the value of of q if p= 45
That'll be when x=30, q=5, and y=120.



Edwin