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Complement of a Set

The following...

Question

The following information is given sets A, B which are subsets of universal set U.

n(U) = 47

n(A) = 18

n(B) = 11, n(A ∩ B) = 10

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

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Solution

The correct option is B
28

Then, the number of elements that are neither in A nor in B is given by n(A^I ∩ B^I)

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

= n(U) - [n(A) + n(B) - n(A∩B)]

= 47 - [18 + 11 - 10]

= 47 - 19

= 28

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