Find n(A∩B)
Question:
If \( A \) and \( B \) are two sets such that
\[ n(A\cup B)=50,\quad n(A)=28,\quad n(B)=32 \]find \( n(A\cap B) \).
Solution
\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \] \[ 50=28+32-n(A\cap B) \] \[ 50=60-n(A\cap B) \] \[ n(A\cap B)=60-50 \] \[ n(A\cap B)=10 \]Hence,
\[ \boxed{n(A\cap B)=10} \]