Given 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

(3)

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

$= 20 - (n (A) + n (B) - n (A \cap B)) = 20 - (12 + 9 - 4) = 20 - 17 = 3$

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 ______.

Ans.
(3)

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

$= 20 - (n (A) + n (B) - n (A \cap B)) = 20 - (12 + 9 - 4) = 20 - 17 = 3$

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Solution

Q. 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 ______.

Ans. (3) n[(A∪B)c]=n(U)-n(A∪B) =20-(n(A)+n(B)-n(A∩B))=20-(12+9-4)=20-17=3

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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 ______.

Ans.
(3)

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

$= 20 - (n (A) + n (B) - n (A \cap B)) = 20 - (12 + 9 - 4) = 20 - 17 = 3$