Let A and B be two sets such that
\[ n(A)=16,\quad n(B)=14,\quad n(A\cup B)=25 \]
Then, \(n(A\cap B)\) is equal to
(a) 30
(b) 50
(c) 5
(d) none of these
Solution
Using the formula,
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]
Substituting the values,
\[ 25=16+14-n(A\cap B) \]
\[ 25=30-n(A\cap B) \]
\[ n(A\cap B)=30-25 \]
\[ =5 \]
Answer
\[ \boxed{5} \]
Correct option: (c)