Number of Elements in Union and Intersection of Sets

Q.

In a school all the students have to learn drawing or painting. If 36% of the students learn drawing and painting and 40% of those who learn drawing do not learn painting, then what % of the students learn painting?

1. 40%

2. 60%

3. 76%

4. 80%

Q. If n(A - B) = 36, n(B - A) = 40 and n $(A\cap B)=24,$ then n $(A\cup B)=$ ___

1. 100
2. 64
3. 60
4. 76

Q.

Match the following:

Given U is universal set.

A, B are subsets of U.

n(U), n(A), n(B) are the cardinal numbers of U, A and B respectively.

Number of:

1. A - i, B - iv, C - ii, D- iii

2. A - iii, B - iv, C - ii, D- i

3. A - iii, B - iv, C - i, D- ii

4. A - ii, B - iv, C - iii, D- i

Q. In a factory, all the workers like oranges and apples. If 70% of the workers like oranges and 64% likes apples and x % like both apples and oranges, then x = ______.

1. 34%
2. 36%
3. 70%
4. 64%

Q.

A is a subset of B. If n(A) = 10 and n(B) = 30, then n(B U A) = __________ .

1. 10

2. 20

3. 30

4. 40

Q.

In a class of 30 students, 18 students play cricket, 15 students play football 12 play both the games. How many students in the class don't play both the games?

__

Q. Of a total of 300 users who make video calls, 75 people use Viber, 45 use Skype and 30 use both. The no. of people who use neither Viber nor Skype is

1. $210$
2. $150$
3. $270$

Q.

In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people have listened to Pink Floyd. 30 people have listened to metallica and 20 people have listened to John Denver. If 10 people have listened to all three then find the no. of people who have listened only Pink Floyd.

1. 10

2. 20

3. 30

4. 25

Q.

In a mathematics class, 20 children had forgotten their rulers and 17 forgotten their pencils. "Go and borrow them from someone at once”, said the teacher. If 24 children left the room, then the number of children who had forgotten both is ____.

1. 11

2. 12

3. 13

4. 14

Q.

If $n(\cup )=700$, $n\left(A\right)=200$, $n\left(B\right)=300$ , $n(A\cap B)=100$, then $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})$

1. 400

2. 240

3. 300

4. 500

Q.

In a city 20% of the population travel by car, 50% travel by bus and 10% travel by both car and bus. The percentage of the population traveling by car or bus is ____.

1. 70%

2. 80%

3. 40%

4. 60%

Q.

In a factory all the workers like oranges or apples. If $70\%$ of the workers like oranges and $64\%$ likes apples and $x\%$ like both oranges and apples, then x = ____.

1. 34%

2. 36%

3. 64%

4. 70%

Q.

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of persons speaking at least one of these two languages is _____.

1. 38

2. 58

3. 40

4. 60