If A and B are subsets of universal set U such that n(U) = 800, n(A) = 300, n(B) = 400 and n(A ∩ B) = 100. The number of elements in the set Ac ∩ Bc is

Question

If A and B are subsets of universal set U such that n(U) = 800, n(A) = 300, n(B) = 400 and n(A ∩ B) = 100. The number of elements in the set Ac ∩ Bc is (A) 100 (B) 200 (C) 300 (D) 400

Tardigrade Admin · Accepted Answer

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 300 + 400- 100 = 600 n(A ∪ B)c = n(U) - n(A ∪ B) = 800 - 600 = 200

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

$100$

$200$

$300$

$400$

$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 300 + 400 - 100 = 600$
$n (A \cup B)^{c} = n (U) - n (A \cup B) = 800 - 600 = 200$

Q. If A and B are subsets of universal set U such that n(U)=800, n(A)=300, n(B)=400 and n(A∩B)=100. The number of elements in the set Ac∩Bc is

100

200

300

400