For universal set $\cup$ , and sets A, B which are subsets of $\cup$ , the following information is given

n(U) = 47

n(A) = 18

n(B) = 11, n(A $\cap$ B) = 10

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

_

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Solution

n(A^I $\cap$ B^I) = n(A $\cup$ B)^I= n(U) - n(A $\cup$ B)

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

= 47 - [18 + 11 - 10]

= 47 - 19

= 28

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