Exam

JEE Main

Subject

Mathematics

Chapter

Sets and Relations

JEE Main · Mathematics · Sets and Relations

array l If A and B are subsets of universal set X such that...

\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}

Step-by-step solution

$$\begin{aligned}n\left(A \cap B^{\prime}\right) \text{ and } =n(A)-n(A \cap B) \\ n(x) \text{ and } =200 \\ \text{ and } \sim(A \cap B)=n(A)+n(B)+2\left(A^{\prime} \cap B^{\prime}\right) \\ &-n(X) \\ n\left(A \cap B^{\prime}\right) \text{ and } =90-10 \\ \text{ and } =80 \end{aligned}$$