If A and B are two disjoint sets, then \(n(A \cup B)\) is equal to
(a) \(n(A)+n(B)\)
(b) \(n(A)+n(B)-n(A\cap B)\)
(c) \(n(A)+n(B)+n(A\cap B)\)
(d) \(n(A)n(B)\)
Solution
For disjoint sets,
\[ A\cap B=\Phi \]
Therefore,
\[ n(A\cap B)=0 \]
Using the formula,
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]
\[ =n(A)+n(B)-0 \]
\[ =n(A)+n(B) \]
Answer
\[ \boxed{n(A)+n(B)} \]
Correct option: (a)