Question # 01: Four option are given against each statement. Encircle the correct option.
\((vi)\) If \(n( A\cup B)=50\), \(n( A) =30\) and \(n( B) =35\), then \(n( A\cap B) =\) :
\( a) \quad \) \( 23\)
\( b) \quad \) \( 15\)
\(c) \quad \) \( 9\)
\( d) \quad \) \( 40\)
Answer: \( b) \; \) \( 15\)
Explanation:
Since
\(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)
After rearranging, we get
\(n(A\cap B)=n(A)+n(B)-n(A\cup B)\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =30+35-50\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =15\)