Odisha Board Solutions for Chapter: Sets, Exercise 2: Exercises- 2(b)

Prove that

$|A\cup B\cup C|=\left|A\right|+\left|B\right|+\left|C\right|+|A\cap B\cap C|-|A\cap B|-|B\cap C|-|C\cap A\mid$

If $X$ and $Y$ are two sets such that $X\cup Y$ has $20$ objects, $X$ has $10$ objects and $Y$ has $15$ objects; how many objects does $X\cap Y$ have ?

In a group of $450$ people, $300$ can speak Hindi and $250$ can speak English. How many people can speak both Hindi and English ?

In a group of people, $37$ like coffee, $52$ like tea and each person in the group likes at least one of the two drinks. $19$ people like both tea and coffee, how many people are in the group?

In a class of $35$ students, each student likes to play either cricket or hockey. $24$ students like to play cricket and $5$ students like to play both the games; how many students play hockey?

In a class of $400$ students, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice?

In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

In a survey it was found that $21$ people liked product $A$, $26$ liked product $B$ and 29 liked product $C$. If $14$ people liked products $A$ and $B$, $12$ people liked products $C$ and $A$, $14$ people liked products $B$ and $C$ and $8$ liked all the three products. Find how many liked products $C$ only.