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$\begin{array}{l}
\text { If } \mathrm{A} \text { and } \mathrm{B} \text { are subsets of universal set } \mathrm{X} \text { such that } \mathrm{n}(\mathrm{X})=200, \mathrm{n}(\mathrm{A})=90, \mathrm{n}(\mathrm{B})=80 \text { , }\\
n\left(A^{\prime} \cap B^{\prime}\right)=40, \text { then } n\left(A \cap B^{\prime}\right)=
\end{array}$
Options:
\text { If } \mathrm{A} \text { and } \mathrm{B} \text { are subsets of universal set } \mathrm{X} \text { such that } \mathrm{n}(\mathrm{X})=200, \mathrm{n}(\mathrm{A})=90, \mathrm{n}(\mathrm{B})=80 \text { , }\\
n\left(A^{\prime} \cap B^{\prime}\right)=40, \text { then } n\left(A \cap B^{\prime}\right)=
\end{array}$
Solution:
1719 Upvotes
Verified Answer
The correct answer is:
80
$$
\begin{aligned}
n\left(A \cap B^{\prime}\right) &=n(A)-n(A \cap B) \\
n(x) &=200 \\
& \sim(A \cap B)=n(A)+n(B)+2\left(A^{\prime} \cap B^{\prime}\right) \\
&-n(X) \\
n\left(A \cap B^{\prime}\right) &=90-10 \\
&=80
\end{aligned}
$$
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