If A and B are two sets such that n (A) =20,
Question:

If $A$ and $B$ are two sets such that $n(A)=20, n(B)=25$ and $n(A \cup B)=40$, then write $n(A \cap B)$.

Solution:

We have:

$n(A)=20, n(B)=25$ and $n(A \cup B)=40$

We know:

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

$\Rightarrow n(A \cap B)=n(A)+n(B)-n(A \cup B)$

$=20+25-40$

$=5$

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