Question 1185201: Draw a Venn diagram and use the given information to fill in the number of elements in each region. n(A)=15, n(A ∩ B ∩ C)=6, n(A ∩ C)=13, n(A ∩ B′)=8, n(B ∩ C)=11, n(A′ ∩ B′ ∩ C′)=19, n(B ∩ C′)=3, n(B ∪ C)=33
Answer by Edwin McCravy(20054)   (Show Source):
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n(A ∩ B ∩ C)=6, n(A′ ∩ B′ ∩ C′)=19, so h=6, k=19
n(A ∩ C)=13 = g+h, and since h=6, g=13-6=7
n(B ∩ C)=11 = h+i, and since h=6, i=11-6=5
n(A ∩ B′)=8 = d+g, and since g=7, d=8-7=1
n(A)=15 = d+e+g+h, and since d=1, g=7, and h=6, e=15-1-7-6 = 1
n(B ∩ C′)=3 = e+f, and since e=1, f=3-1=2
n(B ∪ C)=33 = e+f+g+h+i+j, and since e=1, f=2, g=7, h=6, i=5,
j = 33-1-2-7-6-5 = 12
Edwin
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