Use the given information to complete the solution of the pa

Use the given information to complete the solution of the partially solved Venn diagram. HINT [See Example 4.] n(A) = 20, n(B) = 19, n(C) = 28, n(B C) = 7, n(S) = 51

x =

y =

z =

w =

t =

Solution

X = n (A) - ( 4 + 2 + 10) = 20 - 16 = 4

Y = n (B) - ( 4 + 2 + w) = 19 - 6 - W = 13 - W : W = n(B C) - 2 = 7 - 2 = 5 so that Y = 13 - 5 = 8

Z = n (C) - ( 2 + 10 + W) = 28 - 12 - W = 16 - W = 16 - 5 = 11

W = 5 ( as above)

t = n (S) - [ n(A) + n (B) + n (C)] = 51 - ( 20 + 19 + 28) + ( 4 + 2 +10 + W) = 51 - 67+ ( 16 + 5) = 51 + 21 - 67 = 72 - 67 = 5