SET REVISION QUESTIONS WITH ANSWERS

Set Theory: 30 Questions (Two Sets)

1. Given \( A = \{1, 2, 3, 4\} \) and \( B = \{3, 4, 5, 6\} \), find \( A \cap B \).

2. Let \( A = \{x : x \text{ is even}, x \leq 10\} \) and \( B = \{x : x \text{ is a multiple of 3}, x \leq 10\} \). Find \( A \cup B \).

3. If \( A = \{a, b, c\} \) and \( B = \{c, d\} \), list \( A - B \).

4. Determine whether \( A \subseteq B \), where \( A = \{2, 4\} \) and \( B = \{1, 2, 3, 4, 5\} \).

5. If \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{6, 7\} \), are the sets disjoint?

6. Find the number of elements in \( A \cup B \) if \( n(A) = 6 \), \( n(B) = 7 \), and \( n(A \cap B) = 3 \).

7. In a Venn diagram of two sets \( A \) and \( B \), what region represents \( A \cap B \)?

8. If \( A = \{2, 4, 6, 8\} \) and \( B = \{1, 3, 5, 7\} \), find \( A \cup B \).

9. Let \( A = \{x : x \in \mathbb{N}, x < 5\} \) and \( B = \{x : x > 2\} \), find \( A \cap B \).

10. If \( A = \{a, b\} \) and \( B = \{a, b, c\} \), is \( A \subset B \)?

11. Find the symmetric difference \( A \Delta B \) for \( A = \{1, 2\} \), \( B = \{2, 3\} \).

12. Given \( A \cup B = \{1, 2, 3, 4, 5\} \) and \( A \cap B = \{3\} \), find possible sets \( A \) and \( B \).

13. Find \( n(A \cup B) \) given \( n(A) = 10 \), \( n(B) = 15 \), and \( n(A \cap B) = 5 \).

14. Let \( U = \{1, 2, 3, 4, 5, 6\} \), \( A = \{2, 4\} \), find \( A' \).

15. If \( A = \{x : x \text{ is a prime } \leq 10\} \), and \( B = \{2, 4, 6, 8\} \), find \( A \cap B \).

16. Draw a Venn diagram showing \( A \cup B \).

17. Use a Venn diagram to show that \( A \subset B \).

18. Let \( A = \{x : x \text{ is a vowel}\} \) and \( B = \{a, e, i, o, u, y\} \). What is \( A \cap B \)?

19. Find the universal set \( U \) that contains both \( A = \{1, 2\} \) and \( B = \{2, 3, 4\} \).

20. Is \( \{0\} \subseteq \{0, 1, 2\} \)?

21. Find elements in \( B - A \), where \( A = \{2, 4\} \) and \( B = \{2, 3, 4, 5\} \).

22. What is \( (A \cup B)' \) if \( U = \{1, 2, 3, 4, 5, 6\} \), \( A = \{1, 2\} \), \( B = \{3, 4\} \)?

23. Let \( A = \{x : x \text{ divisible by 2 and } \leq 10\} \), \( B = \{x : x \text{ divisible by 3 and } \leq 10\} \). Find \( A \cap B \).

24. Use a Venn diagram to explain \( A - B \).

25. Show with a Venn diagram that \( A \cap B = B \cap A \).

26. Prove using example that \( A \cup B = B \cup A \).

27. Identify the shaded region of a Venn diagram with \( A \cup B \).

28. If \( A = \{\text{days of the week}\} \) and \( B = \{\text{weekend days}\} \), find \( A - B \).

29. Let \( A = \{\text{even numbers}\} \), \( B = \{\text{odd numbers}\} \), what is \( A \cap B \)?

30. If \( A = \{\text{Multiples of 2}\} \) and \( B = \{\text{Multiples of 4}\} \), what is \( A \cap B \)?

Answers:

1. \(\{3, 4\}\)
2. \(\{2, 4, 6, 8, 10, 3, 9\}\)
3. \(\{a, b\}\)
4. Yes
5. Yes, disjoint
6. 10
7. Overlapping area of the two circles
8. \(\{1, 2, 3, 4, 5, 6, 7, 8\}\)
9. \(\{3, 4\}\)
10. Yes
11. \(\{1, 3\}\)
12. Various correct possibilities
13. 20
14. \(\{1, 3, 5, 6\}\)
15. \(\{2\}\)
16. Venn diagram with union shaded
17. One circle inside another
18. \(\{a, e, i, o, u\}\)
19. \(\{1, 2, 3, 4\}\)
20. Yes
21. \(\{3, 5\}\)
22. \(\{5, 6\}\)
23. \(\{6\}\)
24. Venn diagram shading left side only
25. Overlapping area shaded
26. True
27. Entire union area shaded
28. \(\{\text{Mon, Tue, Wed, Thu, Fri}\}\)
29. \(\emptyset\)
30. \(\{\text{Multiples of 4}\}\)