Question

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

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

Answer: (B)

$200$

Answer 2

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