A & B are subsets of universal set U such that n(U) = 800, n(A) = 300, n(B) = 400 & n(A ? B) = 100. The number of elements in the set A? ? B is

Question

$A$ & $B$ are subsets of universal set $U$ such that $n (U) = 800$ , $n (A) = 300$ , $n (B) = 400$ & $n (A \cap B) = 100$ . The number of elements in the set $A^{c} \cap B^{c}$ is

Smart Achievers · Accepted Answer

(2)

$B$ $= 300 + 400 - 100 = 600$

$n {(A \cup B)}^{c} = n (U) - n (A \cup B) = 800 - 600 = 200$

$∴$ $n (A^{c} \cap B^{c}) = n {(A \cup B)}^{c} = 200$

Solution

Q.
$A$ & $B$ are subsets of universal set $U$ such that $n (U) = 800$ , $n (A) = 300$ , $n (B) = 400$ & $n (A \cap B) = 100$ . The number of elements in the set $A^{c} \cap B^{c}$ is

1 100

2 200

3 300

4 400

Ans.
(2)

$n (A \cup B) = n (A) + n (B) - n (A \cap B)$ $= 300 + 400 - 100 = 600$

$n {(A \cup B)}^{c} = n (U) - n (A \cup B) = 800 - 600 = 200$

$∴$ $n (A^{c} \cap B^{c}) = n {(A \cup B)}^{c} = 200$

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