For universal set U, and sets A, B which are subsets of U, the following information is given -

n(U) = 47

n(A) = 18

n(B) = 11

n(A ∩ B) = 10

Then, the number of elements that neither in A nor B are __

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Solution

n(A^I ∩ B^I) = n(A U B)^I= n(U) - n(A U B)

$= n (U) - [n (A) + n (B) - n (A \cap B)]$

$= 47 - [18 + 11 - 10]$

$= 47 - 19$

$= 28$

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