Directions: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z). which is equal to 90.
What is the value of n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z)?
a + b + 106
Calculation:
Given: n(Z) = 90,
From above diagram, we get
n(X) = a + 46, n(Y) = b + 51, n(X ∩ Y) = 16 + 18 = 34, n(Y ∩ Z) = 17 + 18 =35, n(X ∩ Z) = 12 + 18 = 30, n(X ∩ Y ∩ Z) = 18
n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z) =
a + 46 + b + 51 + 90 - 34 - 35 - 30 + 18
= a + b + 106
Hence, option (4) is correct.
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