Question Detail
Question
If \( n(A) = p \), \( n(B) = q \), \( n(U) = N \), and \( A \cap B = \emptyset \), then \( n(A^c \cap B^c) = ? \)
Correct Answer
Option A is the correct answer.
Detailed Explanation
Since A and B are disjoint, n(A ∪ B) = p + q. Then A^c ∩ B^c = (A ∪ B)^c by De Morgan's Law. So n((A ∪ B)^c) = n(U) - n(A ∪ B) = N - (p+q) = N - p - q.
Hint
Use De Morgan's Law: (A^c ∩ B^c) = (A ∪ B)^c. Then complement formula.