Amit M Agarwal Solutions for Chapter: Sets, Exercise 3: Entrances Gallery

The shaded region in the figure represents 

If $n\left(A\right)=1000, n\left(B\right)=500$ and if $n\left(A\cap B\right)\ge 1$ and $n\left(A\cup B\right)=p$, then 

Out of $64$ students, the number of students taking Mathematics is $45$ and the number of students taking both Mathematics and Biology is $10$. Then, the number of students taking the only Biology is

There are $100$ students in a class. In the examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects is

The set $A=\left\{x : x\in R, x^2=16 \text{and} 2x=6\right\}$ is equal to

Let $A$ and $B$ be two sets, then $(A\cup B{)}^{\text{'}}\cap \left(A^{\text{'}}\cap B\right)$ is equal to

Let $A=\left\{1, 2\right\}, B=\left\{\left\{1\right\}, \left\{2\right\}\right\}, C=\left\{\left\{1, 2\right\}\right\}$. Then which of the following relation is true?

$25$ people employed for the program $A$, $50$ people for the program $B$, $10$ people for both $A \& B$. So, the number of employees employed for only $A$ is