Properties of Set Operation

Q. Let $A=\{1,2,3\}$ and $R,S$ be two relations on $A$ given by $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1\left)\right\},S=\left\{\right(1,1),(2,2),(3,3),(2,3),(3,2\left)\right\}$ then $R\cup S$ is

1. Reflexive, symmetric and transitive relation
2. reflexive and transitive relation only
3. Reflexive relation but not Symmetric relation
4. not a transitive relation

Q. Sam and Alex plays in the same soccer team. Last saturday Alex scored $3$ more goals than Sam, but together they scored less than $9$ goals. The possible number of goals that Alex scored?

1. $2$
2. $3$
3. $4$
4. $6$

Q. In a school three languages English, French and Spanish are taught. $30$ students study English, $25$ study French and $20$ study Spanish. Although no student studies all three languages, $8$ students study both English and French, $5$ students study both French and Spanish and $7$ students study both Spanish and English. How many students study at least one of the three languages?

1. $50$
2. $60$
3. $45$
4. $55$

Q. Let $A$ and $B$ are two sets. Then $n(A^C\cap B^C)=$

1. $n\left(U\right)–n(A\cap B)$
2. $n\left(U\right)–n(A\cup B)$
3. $n\left(U\right)–n(A^C\cup B)$
4. $n\left(A\right)+n\left(B\right)$

Q. A group of $123$ workers went to a canteen for cold drinks, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drinks. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drinks, and $4$ purchased cold drinks and tea but not ice-cream. Then the number of workers who did not purchase anything is

Q. For any three sets $A,B\&C,$
$n(A\cup B\cup C)=n\left(A\right)+n\left(B\right)+n\left(C\right)$
$-n(A\cap B)-n(B\cap C)-n(C\cap A)$
$+n(A\cap B\cap C)$

1. False
2. True

Q. In a group of $70$ people, $37$ like coffee, $52$ like tea and each person like atleast one of the two drinks. The number of persons liking both coffee and tea is

1. $16$
2. $13$
3. $19$
4. $20$

Q. In a class of $100$ students, $55$ students have passed in Maths, $67$ passed in Physics. If all the students pass in at least one subject, then the number of students who passed in physics only is

1. $22$
2. $33$
3. $10$
4. $45$

Q.

Find the value of $150\%$ of $75$.

Q. If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

1. $B\subseteq A$
2. $A\subseteq B$
3. $A=B$
4. $A\cap B=A$

Q.

In a survey of 200 students from 7 different schools, 50 people do not play NFS, 40 people do not play Dota and 10 people play no online game. Then find the no. of people out of 200 people who do not play both the games provided these are the only two games on offer.

1. 80

2. 70

3. 60

4. 50

Q. If $n\left(A\right)=n\left(B\right),$ then which of the following is correct?

1. $n(A–B)=n(B–A)$
2. $n(A\cup B)=n\left(A\right)+n\left(B\right)$
3. $n(A\cap B)=n\left(B\right)+n(A–B)$
4. $n(A–B)=n(A\cap B)$

Q.

In a factory $70\text{\%}$ of the workers like oranges and $64\text{\%}$ likes apples. If each worker likes at least one fruit, What is the minimum percentage of workers who like both the fruits?

1. $34$
2. $32$
3. $35$
4. $33$

Q. A group of $123$ workers went to a canteen for cold drinks, ice-cream and tea. $42$ workers took ice-cream, $36$ took tea and $30$ took cold drinks. $15$ workers purchased ice-cream and tea, $10$ purchased ice-cream and cold drinks, and $4$ purchased cold drinks and tea but not ice-cream. Then how many workers did not purchase anything ?

1. $44$
2. $46$
3. $48$
4. $42$

Q. Let $A=\{1,2,3,4\},$ $B=\{2,3,4,5,6\},$ then $A\Delta B$ is

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

Q. In a group of tourists, $40\%$ liked Goa, $30\%$ liked Kerala and $30\%$ liked Bangalore. $7\%$ liked both Goa and Kerala, $5\%$ liked both Kerala and Bangalore, $10\%$ liked both Bangalore and Goa. If $86\%$ of these liked at least one of the places, then what percentage of people liked all three?

1. $5$
2. $6$
3. $7$
4. $8$

Q. Let $A=\{1,2,3,4\},$ $B=\{2,3,4,5,6\},$ then $A\Delta B$ is

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

Q. In a community it is found that $52\%$ people like prime video and $73\%$ like Netflix and $x\%$ like both, then $x$ can be

1. $21$
2. $32$
3. $52$
4. $62$

Q.

Compare $15\%$ of $6800$ and $12\%$ of $7500$, which is more and by how much?

Q. In a community it is found that $52\%$ people like prime video and $73\%$ like Netflix and $x\%$ like both, then $x$ can be

1. $21$
2. $32$
3. $52$
4. $62$

Q. For any two sets $A\&B,$
$A\cup B=\{x:x\in A\text{or}x\in B\}$
$A\cap B=\{x:x\in A\text{and}x\in B\}.$

1. False
2. True

Q. Let $X=\{n\in N:1\le n\le 50\}$. If $A=\{n\in X:n\text{is a multiple of 2}\}$ and $B=\{n\in X:n\text{is a multiple of 7}\}$, then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

Q. In a class of $400$ students, $150$ are interested in doing a statistics project, $300$ are interested in doing a machine learning project and $25$ are not interested in doing either of the projects. Then the number of students who are interested in doing both the projects, is

1. $50$
2. $75$
3. $125$
4. $65$

Q. In a survey of $200$ students of a higher secondary school, it was found that $120$ studied mathematics; $90$ studied physics and $70$ studied chemistry; $40$ studied mathematics and physics; $30$ studied physics and chemistry; $50$ studied chemistry and mathematics, and $20$ studied none of these subjects. Then the number of students who studied all the three subjects, is

1. $20$
2. $12$
3. $30$
4. $15$

Q. In a survey of $200$ students of a higher secondary school, it was found that $120$ studied mathematics; $90$ studied physics and $70$ studied chemistry; $40$ studied mathematics and physics; $30$ studied physics and chemistry; $50$ studied chemistry and mathematics, and $20$ studied none of these subjects. Then the number of students who studied all the three subjects, is

1. $20$
2. $12$
3. $30$
4. $15$

Q. In a town of 10, 000 families it was found that $40\%$ family buy newspaper A, $20\%$ buy newspaper B and $10\%$ families buy newspaper C, $5\%$ families buy A and B, $3\%$ buy B and C and $4\%$ buy A and C. If $2\%$ families buy all the three newspapers, then number of families which buy A only is

1. 3100
2. 3300
3. 2900
4. 1400