Given n ( U ) = 20 , n ( A ) = 12 , n ( B ) = 9 , n ( A B ) = 4 , where U is the universal set, A and B are subsets of U , then n [ ( A B ) c ] equals to

Question

Given $n (U) = 20$ , $n (A) = 12$ , $n (B) = 9$ , $n (A \cap B) = 4$ , where $U$ is the universal set, $A$ and $B$ are subsets of $U$ , then $n [{(A \cup B)}^{c}]$ equals to

Smart Achievers · Accepted Answer

(4)

$n [{(A \cup B)}^{C}] = n (U) - n (A \cup B)$

$= 20 - (n (A) + n (B) - n (A \cap B))$

$= 20 - (12 + 9 - 4) = 20 - 17 = 3$

Solution

Q.
Given $n (U) = 20$ , $n (A) = 12$ , $n (B) = 9$ , $n (A \cap B) = 4$ , where $U$ is the universal set, $A$ and $B$ are subsets of $U$ , then $n [{(A \cup B)}^{c}]$ equals to

1 17

2 9

3 11

4 3

Ans.
(4)

$n [{(A \cup B)}^{C}] = n (U) - n (A \cup B)$

$= 20 - (n (A) + n (B) - n (A \cap B))$

$= 20 - (12 + 9 - 4) = 20 - 17 = 3$

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