If A and B are two sets such that


If $A$ and $B$ are two sets such that $n(A)=23, n(b)=37$ and $n(A-B)=8$ then find $n(A \cup B)$

$\operatorname{Hint} n(A)=n(A-B)+n(A \cap B) n(A \cap B)=(23-8)=15 .$



Given: $n(A)=23, n(B)=37, n(A-B)=8$

Using the hint

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

$\Rightarrow 23=8+n(A \cap B)$

$\Rightarrow n(A \cap B)=23-8$

$\Rightarrow n(A \cap B)=15$

Visualizing the hint given,

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

$\Rightarrow n(A \cup B)=23+37-15$

$\Rightarrow \mathrm{n}(\mathrm{A} \cup \mathrm{B})=45$

Hence $n(A \cup B)=45$

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