Venn Diagrams

Q.

A survey shows that $63\%$ of the people in a city read newspaper $A$ whereas $76\%$ read newspaper $B$. If $x\%$ of the people read both the newspapers, then a possible value of $x$ can be:

$37$

$29$

$65$

$55$

Q.

If $\text{A}$ and $\text{B}$ are two events such that $\text{P(AUB)}$$=$$\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, $\text{P(A∩B)}$$=$$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$, $\text{P(A’)}$$=$$\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, then $\text{P(A’∩B)}$ is equal to

1. $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$

2. $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$

3. $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$

4. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Q.

If $\text{A}$ and $\text{B}$ are two events such that $\text{P(AUB)}$$=$$\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$, $\text{P(A∩B)}$$=$$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, and $\text{P(B)}$$=$$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, then $\text{P(A)}$$=?$

1. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

2. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

3. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

4. $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

Q. If $X$ and $Y$ are two sets then $X\cap (Y\cup X{)}^{\prime }$ equals

1. $X$
2. $Y$
3. $\varphi$
4. none of these

Q. In the following diagram, the shaded part represents

1. $(A-B{)}^C\cap (B-C)$
2. $(A-B)\cap (B-C{)}^C$
3. $(A-B{)}^C\cap (B-C{)}^C$
4. $(A-B)\cap (C-B)$

Q. A survey shows that $63\%$ of the people in a city read newspaper $A$ whereas $76\%$ read newspaper $B$. If $x\%$ of the people read both the newspapers, then a possible value of $x$ can be

1. $37$
2. $29$
3. $65$
4. $55$

Q. In a group of $115$ people, each has at least one among passport and voter ID. If $65$ had passport and $30$ had both, how many had only voter ID but not passport?

1. $30$
2. $50$
3. $80$
4. $55$

Q. A factory has $80$ workers and $3$ machines. Each worker knows to operate at least two machines. If there are $65$ persons who know to operate machine $\text{I},$ $60$ for machine $\text{II}$ and $55$ for machine $\text{III},$ then the minimum number of persons who know to operate all the three machines is

Q. From the adjoining venn diagram, find $(A\cup B)\cap C$

1. $\{1,3,4,5\}$
2. $\{1,5,6\}$
3. $\{5,6\}$
4. $\left\{5\right\}$

Q. For the three events $A,$ $B$ and $C,$ $P\text{(at least one occurring)}=\frac{3}{4},$ $P\text{(at least two occurring)}=\frac{1}{2}$ and $P\text{(exactly two occurring)}=\frac{2}{5}.$ Which of the following relations is (are) CORRECT ?

1. $P(A\cap B\cap C)=\frac{1}{10}$
2. $P(A\cap B)+P(B\cap C)+P(C\cap A)=\frac{7}{5}$

3. $P\left(A\right)+P\left(B\right)+P\left(C\right)=\frac{27}{20}$

4. $P(A\cap \overline{B}\cap \overline{C})+P(\overline{A}\cap \overline{B}\cap C)+P(\overline{A}\cap B\cap \overline{C})=\frac{1}{4}$

Q. In a class of $35$ students, $17$ have Chemistry, $10$ have Chemistry but not Physics. If each student of the class has taken either Chemistry or Physics or both, then which of the following is/are true?

1. Number of students taking both Chemistry and Physics is $7$.
2. Number of students taking both Chemistry and Physics is $9$.
3. Number of students taking Physics but not Chemistry is $18$.
4. Number of students taking Physics but not Chemistry is $20$.

Q. The correct representation of three sets $A=\{q,w,e,r,t\}$
$B=\{r,t,y,u,i\}\&C=\{u,q,o,p,t\}$ is

1. 
2. 
3. 
4. 

Q. $A$ is the set of letters of the word $apple,$
$B$ is the set of letters of the word $pineapple,$
$C$ is the set of letters of the word $kiwi,$ then choose the correct statement.

1. $A\cup B=\{p,i,n,e,a,p,p,l,e\}$
2. $A\cup B=\{p,i,n,e,a,l\}$
3. $A\cup C=\{a,p,p,l,e,k,i,w,i\}$
4. $A\cup C=\{a,p,l,e,k,w,i\}$

Q. Let $n(A–B)=25+X,n(B–A)=2X$ and $n(A\cap B)=2X.$ If $n\left(A\right)=2\left(n\right(B\left)\right),$ then $X$ is

1. $4$
2. $5$
3. $6$
4. $7$

Q. $A$ is the set of letters of the word $apple,$
$B$ is the set of letters of the word $pineapple,$
$C$ is the set of letters of the word $kiwi,$ then choose the correct statement.

1. $A\cup B=\{p,i,n,e,a,p,p,l,e\}$
2. $A\cup B=\{p,i,n,e,a,l\}$
3. $A\cup C=\{a,p,p,l,e,k,i,w,i\}$
4. $A\cup C=\{a,p,l,e,k,w,i\}$

Q. At a school, some students like Physics, some like Mathematics and some like both the subjects. Then, choose the best representation of the scenario using venn diagrams.

1. 
2. 
3. 
4. 

Q. Out of $60$ students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, $16$ do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. Then the range of cardinal number of students who could have done only chemistry is

1. $[0,40]$
2. $[0,44]$
3. $[2,28]$
4. $[2,38]$

Q. From the adjoining figure, $A\cap B$ is

1. $\{8,5\}$
2. $\{8,5,0\}$
3. $\{1,5\}$
4. $\{0,1,2,3,5,8,9\}$

Q. Out of 260 students in a class of a school, 135 like tea, 110 like coffee and 80 like milk, 35 of these like both tea and coffee, 30 like both tea and milk, 20 like both coffee and milk. Also, each student likes atleast one of the three drinks. How many students like all the three drinks?

1. 30
2. 15
3. 20
4. 25