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If $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are three sets and $\mathrm{U}$ is the universal set such thatn $(\mathrm{U})=700, \mathrm{n}(\mathrm{A})=200, \mathrm{n}(\mathrm{B})=300$ and $\mathrm{n}(\mathrm{A} \cap \mathrm{B})=100$,
then what is the value of $\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right) ?$
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then what is the value of $\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right) ?$
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Verified Answer
The correct answer is:
300
From the given data $\mathrm{n}(\mathrm{U})=700, \mathrm{n}(\mathrm{A})=200, \mathrm{n}(\mathrm{B})=300$ and
$n(A \cap B)=100$
We know that, $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=200+300-100=400$
Now, $\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=\sim(\mathrm{A} \cup \mathrm{B})^{\prime}=\mathrm{n}(\mathrm{U})-\mathrm{n}(\mathrm{A} \cup \mathrm{B})$
$=700-400=300$
$n(A \cap B)=100$
We know that, $n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$=200+300-100=400$
Now, $\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=\sim(\mathrm{A} \cup \mathrm{B})^{\prime}=\mathrm{n}(\mathrm{U})-\mathrm{n}(\mathrm{A} \cup \mathrm{B})$
$=700-400=300$
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