Question:
If $A$ and $B$ are two sets such than $n(A)=8, n(B)=11$ and $n(A \cup B)=14$ then find $n(A \cap B)$.
Solution:
Given: $n(A)=8, n(B)=11, n(A \cup B)=14$
We know that $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$\Rightarrow 14=8+11-n(A \cap B)$
$\Rightarrow 14=19-n(A \cap B)$
$\Rightarrow n(A \cap B)=19-14$
$\Rightarrow n(A \cap B)=5$
Hence $n(A \cap B)=5$
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