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Sets and Venn Diagrams Practice Problems with Solutions - IGCSE Year 11

IGCSE Year 11 | Math | Sets and Venn Diagrams
Name: _________________________ Date: _________________________ Score: _______ / 40

For A = {1, 2, 3} and B = {2, 3, 4}, the union A ∪ B is {1, 2, 3, 4} and the intersection A ∩ B is {2, 3}, so this Year 11 sheet opens with elements that join and elements that overlap. The complement and the empty set appear in the answers.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. If A = {1, 2, 3} and B = {2, 3, 4}, then A ∪ B is
(a) {1, 2, 3, 4}(b) {2, 3}(c) {1, 4}(d) {1, 2, 3}
2. If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B is
(a) {1, 2, 3, 4}(b) {2, 3}(c) {1, 4}(d) {1, 2}
3. The complement of a set A is
(a) The elements in A(b) The elements in the universal set that are not in A(c) The elements in both A and B(d) The empty set
4. The empty set is denoted by
(a) {0}(b) ∅(c) {1}(d) U
5. If A ∩ B = ∅, then the sets A and B are
(a) Equal(b) Disjoint(c) Overlapping(d) Complementary
6. The number of elements in a set A is called its
(a) Cardinality(b) Union(c) Subset(d) Power

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. If A = {1, 2, 3} and B = {3, 4, 5}, write A ∪ B.
8. If A = {1, 2, 3} and B = {3, 4, 5}, write A ∩ B.
9. Write the symbol for the empty set.
10. Define the complement of a set A.
11. Write the number of subsets of a set containing n elements.
12. What does A ∩ B = ∅ tell you about the sets A and B?
13. Write the symbol commonly used for the universal set.
14. Write the set of even numbers that are less than 10.

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. In a class of 30 students, 18 play football and 12 play cricket. If 5 play both, how many students play at least one of the two games?
16. If A = {2, 4, 6, 8} and B = {1, 3, 5, 7}, write A ∪ B and A ∩ B.
17. In a survey, 20 people like tea and 15 like coffee. If 10 like both, how many people like tea or coffee?
18. Write all the subsets of the set {a, b}.
19. A set has 3 elements. Find the number of subsets it has.
20. In a group of 40 students, 25 study Physics and 20 study Mathematics, and 10 study both. How many students study neither subject?

Answer Key

1. a) {1, 2, 3, 4}
2. b) {2, 3}
3. b) The elements in the universal set that are not in A
4. b) ∅
5. b) Disjoint
6. a) Cardinality
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is A ∪ B when A = {1, 2, 3} and B = {2, 3, 4}?

{1, 2, 3, 4}, option (a) in this worksheet (Q1).

What is A ∩ B when A = {1, 2, 3} and B = {2, 3, 4}?

{2, 3}, option (b) in this worksheet (Q2).

What is the complement of A in the universal set?

The elements in the universal set not in A, option (b) in this worksheet (Q3).

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