Properties of Set Operation

Q.

In a class of 58 students, 20 follow cricket, 38 follow hockey and 15 follow basketball. Three students follow all the three games. How many students follow exactly two of these three games?

__

Q. If A, B and C are any three sets, then $A-(B\cup C)$ is equal to

1. $(A-B)\cap (A-C)$
2. $(A-B)\cup C$
3. $(A-B)\cap C$
4. $(A-B)\cup (A-C)$

Q. If A, B and C are any three sets, then $A\times (B\cap C)$ is equal to

1. $(A\times B)\cap (A\times C)$
   
2. $(A\cup B)\times (A\cup C)$
   
3. $(A\times B)\cup (A\times C)$
   
4. $Noneofthese$

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. 2900
2. 3100
3. 3300
4. 1400

Q.

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is

1. N

2. A

3. $\varphi$

4. B

Q.

${\left[\right(B^{\prime }\cup (B^{\prime }-A)\left)\right]}^{\prime }$ =___

1. A

2. B

3. A - B

4. B - A

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. Let $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$, then $n(A^c\cap B^c)$ equals to

1. $400$
2. $600$
3. $300$
4. $20$

Q. Among a group of students, $50$ played cricket, $50$ played hockey and $40$ played volley ball. $15$ played both cricket and hockey, $20$ played both hockey and volley ball, $15$ played cricket and volley ball and $10$ played all three. If every student played at least one game, then

1. The sum of the number of students who played only cricket, only hockey and only volley ball is $70$
2. The sum of the number of students who played only cricket, only hockey and only volley ball is $75$
3. The number of students who played only cricket is $30$
4. The number of students who played only volley ball is $15$

Q. There are $80$ families in a small town extension area. $20\%$ of these families own a car each. $50\%$ of the remaining families own a motor cycle each. Let $N$ families in that extension do not own any vehicle. Then the value of $\frac{N}{4}$ is