Amit M Agarwal Solutions for Chapter: Sets, Exercise 2: Target Exercises

If $A=\left\{y:y=2x,x\in N\right\}, B=\left\{y:y=2x-1,x\in N\right\}$, then ${\left(A\cap B\right)}^{\text{'}}$ is

If $n\left(A\right)=4$ and $n\left(B\right)=7$, then the minimum and maximum values of $n\left(A\cup B\right)$ are respectively

Let $X$ be the universal set for sets $A$ and $B$. If $n\left(A\right)=200, n\left(B\right)=300$ and $n\left(A\cap B\right)=100$, then $n\left(A^{\text{'}}\cap B^{\text{'}}\right)$ is equal to $300$ provided $n\left(X\right)$ is equal to

Suppose $A_1, A_2,\dots ,A_{30}$ are thirty sets each with five elements and $B_1, B_2,\dots ,B_n$ are $n$ sets each with three elements. Let $\underset{i=1}{\overset{30}{\cup }}{A}_i=\underset{j=1}{\overset{n}{\cup }}{B}_j=S$. Assume that each element of $S$ belongs to exactly $10$ of the ${A_i}^{\text{'}}s$ and exactly $9$ of ${B_j}^{\text{'}}s$. The value of $n$ must be 

If there are three athletic teams in a school; out of all team members $21$ are in the basketball team, $26$ are in the hockey team and $29$ are in the football team; $14$ members play hockey and basketball, $15$ play hockey and football, $12$ members play football and basketball and $8$ members play all the games. Then the total number of members is

In a certain town, $25\%$ families own a phone and $15\%$ own a car, $65\%$ families own neither a phone nor a car. $2000$ families own both a car and a phone.

Consider the following statements in this regard:

I. $10\%$ families own both a car and a phone.

II. $35\%$ families own either a car or a phone.

III. $40000$ families live in the town.

Which of the above statements are correct?

$20$ teachers of a school either teaching mathematics or physics. $12$ of them teaching mathematics, while $4$ teaching both the subjects. Then, the number of teachers teaching physics only are

A survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples, then we have