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

$n (U) = 47,$

$n (A) = 18,$

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

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

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Solution

n(A^c ∩ B^c) = n(A U B)^c[De Morgan's laws]
= 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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