If A and B are two sets such that
\[ n(A)=70,\quad n(B)=60,\quad n(A\cup B)=110 \]
Then, \(n(A\cap B)\) is equal to
(a) 240
(b) 50
(c) 40
(d) 20
Solution
Using the formula,
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]
Substituting the values,
\[ 110=70+60-n(A\cap B) \]
\[ 110=130-n(A\cap B) \]
\[ n(A\cap B)=130-110 \]
\[ =20 \]
Answer
\[ \boxed{20} \]
Correct option: (d)