Worksheet on Cardinal Properties of Sets

In worksheet on cardinal properties of sets we will solve 10 different types of questions on sets.

1. If A and B are two sets such that n(A) = 15, n(B) = 21 and n(A ∪ B) 36, find n(A ∩ B). 

2. If P and Q are two sets such that P ∪ Q has 20 elements, P has 9 elements and Q has 16 elements. How many elements does P ∩ Q have? 

3. In a group of 300 people, 150 can speak French and 200 can speak German. How many can speak both French and German? 

4. If X and Y are two sets such that X has 30 elements, Y has 41 elements and X ∩ Y has 15 elements. How many elements does X ∪ Y have? 

5. If A and B are two sets such that A has 35 elements, A ∪ B has 80 elements and A∩B has 10 elements, how many elements does B have?

6. In a group, 50 persons play basketball, 20 play football and 10 play both. How many play at least one of the two games?

7. There are 600 people residing in a campus. Out of these, 340 people take the Hindustan Times and 270 people take The Times of India. There are 70 persons who take both the papers. Find the number of persons who do not take either of the two papers.

8. In an exam, 70 girls secured first class marks in Science or Math. Out of these, 40 girls secured first class marks in Math and 10 girls in Science and Math. How many girls secured first class marks in Science only?

9. In a group of 90 people, 41 like jogging, 30 like swimming and 8 like jogging and swimming both.


(a) how many like jogging only?

(b) how many like swimming only?

(c) how many like at least one of them?

(d) how many like none of them?

10. In a group of persons, 23 like vanilla ice cream, 19 like strawberry ice cream and 8 like both the ice creams.


(a) the number of persons in the group.

(b) the number of persons who like vanilla ice cream only.

(c) the number of persons who like strawberry ice cream only.

Answers for worksheet on cardinal properties of sets are given below to check the exact answer.


1. 0

2. 5

3. 50

4. 56

5. 55

6. 60

7. 60

8. 30

9. (a) 33
    (b) 22
    (c) 63
    (d) 27

10. (a) 34
     (b) 15
      (c) 11

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