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If $n(A)=115, n(B)=326, n(A-B)=47$, then what is
$\begin{array}{ll}n(A \cup B) \text { equal to? } &\end{array}$
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$\begin{array}{ll}n(A \cup B) \text { equal to? } &\end{array}$
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Verified Answer
The correct answer is:
373
We know, for two sets $\mathrm{A}$ and $\mathrm{B}$ $\mathrm{A}-\mathrm{B}=\mathrm{A}-(\mathrm{A} \cap \mathrm{B})$
$n(A-B)=n(A)-n(A \cap B)$
Given, $n(A)=115, n(B)=326$ and $n(A-B)=47$.
$\Rightarrow 47=115-n(A \cap B)$
$\Rightarrow n(A \cap B)=68$
Consider $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=115+326-68=373$
$n(A-B)=n(A)-n(A \cap B)$
Given, $n(A)=115, n(B)=326$ and $n(A-B)=47$.
$\Rightarrow 47=115-n(A \cap B)$
$\Rightarrow n(A \cap B)=68$
Consider $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=115+326-68=373$
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