Interactive Grade 11 Maths Quiz: Sets | Concept of Maths

Question 1

1. If a set \( A \) has 4 elements, how many non-empty proper subsets does \( A \) have?

A) 16

B) 15

C) 14

D) 13

Answer

Correct Answer: C

Question 2

2. Given \( A = \{x : x^2 - 5x + 6 = 0\} \) and \( B = \{2, 4\} \). Find \( A \Delta B \) (Symmetric Difference).

A) \( \{3, 4\} \)

B) \( \{2, 3, 4\} \)

C) \( \{2\} \)

D) \( \{ \} \)

Answer

Correct Answer: A

Question 3

3. In a class of 50 students, 30 like Cricket, 25 like Football, and 10 like both. How many like neither?

A) 5

B) 10

C) 15

D) 0

Answer

Correct Answer: A

Question 4

4. Let \( A = \{1, 2, \{3, 4\}, 5\} \). Which of the following statements is FALSE?

A) \( \{3, 4\} \in A \)

B) \( \{3, 4\} \subset A \)

C) \( \{\{3, 4\}\} \subset A \)

D) \( \{1, 2\} \subset A \)

Answer

Correct Answer: B

Question 5

5. If \( n(A) = p \) and \( n(B) = q \), what is the maximum number of elements in \( A \cup B \)?

A) \( p + q \)

B) \( \max(p, q) \)

C) \( p \times q \)

D) \( p^q \)

Answer

Correct Answer: A

Question 6

6. Which of the following is an empty set?

A) \( \{x : x \in \mathbb{R}, x^2 - 1 = 0\} \)

B) \( \{x : x \in \mathbb{R}, x^2 + 1 = 0\} \)

C) \( \{0\} \)

D) \( \{\emptyset\} \)

Answer

Correct Answer: B

Question 7

7. If \( U = \{1, 2, 3, ..., 10\} \), \( A = \{1, 3, 5, 7, 9\} \), and \( B = \{2, 4, 6, 8, 10\} \), then \( (A \cup B)' \) is:

A) \( U \)

B) \( \emptyset \)

C) \( \{1, 2, ..., 10\} \)

D) \( \{5, 6\} \)

Answer

Correct Answer: B

Question 8

8. The number of elements in the power set of a power set of an empty set, \( P(P(\emptyset)) \), is:

A) 0

B) 1

C) 2

D) 4

Answer

Correct Answer: C

Question 9

9. If \( A \subset B \), then \( A - B \) is equal to:

A) \( A \)

B) \( B \)

C) \( \emptyset \)

D) \( B - A \)

Answer

Correct Answer: C

Question 10

10. In a survey, 70% of people like Tea, 80% like Coffee. What is the minimum percentage of people who like both?

A) 50%

B) 70%

C) 30%

D) 10%

Answer

Correct Answer: A

Question 11

11. If \( A \) and \( B \) are two sets such that \( n(A-B) = 24 \), \( n(B-A) = 19 \) and \( n(A \cap B) = 11 \), find \( n(A \cup B) \).

A) 43

B) 54

C) 35

D) 65

Answer

Correct Answer: B

Question 12

12. For any two sets \( A \) and \( B \), \( A \cap (A \cup B)' \) is:

A) \( A \)

B) \( B \)

C) \( \emptyset \)

D) \( A \cap B \)

Answer

Correct Answer: C

Question 13

13. Let \( A = \{x : x \in \mathbb{N}, x \text{ is a multiple of 3}\} \) and \( B = \{x : x \in \mathbb{N}, x \text{ is a multiple of 5}\} \). Then \( A \cap B \) is:

A) Multiples of 8

B) Multiples of 15

C) Multiples of 2

D) Empty Set

Answer

Correct Answer: B

Question 14

14. If \( A = \{1, 3, 5\} \) and \( B = \{2, 4\} \), then \( n(P(A \times B)) \) is:

A) 32

B) 64

C) 8

D) 128

Answer

Correct Answer: B

Question 15

15. Which of the following sets is infinite?

A) \( \{x \in \mathbb{Z} : -100 < x < 100\} \)

B) \( \{x \in \mathbb{N} : x \text{ is prime}\} \)

C) The set of months in a year

D) \( \{x \in \mathbb{R} : x^2 - 4 = 0\} \)

Answer

Correct Answer: B

Question 16

16. If \( A, B, C \) are three sets, then \( A \cap (B - C) \) is equal to:

A) \( (A \cap B) - (A \cap C) \)

B) \( (A \cap B) - C \)

C) \( A \cap B \cup C \)

D) Both A and B

Answer

Correct Answer: D

Question 17

17. Two finite sets have \( m \) and \( n \) elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of \( m \) and \( n \) are:

A) 7, 6

B) 6, 3

C) 5, 1

D) 8, 7

Answer

Correct Answer: B

Question 18

18. What is the interval representation of \( \{x : x \in \mathbb{R}, -2 < x \le 5\} \)?

A) \( [-2, 5] \)

B) \( (-2, 5) \)

C) \( (-2, 5] \)

D) \( [-2, 5) \)

Answer

Correct Answer: C

Question 19

19. If \( n(A) = 10 \), \( n(B) = 15 \), then the minimum number of elements in \( A \cup B \) is:

A) 10

B) 15

C) 25

D) 5

Answer

Correct Answer: B

Question 20

20. According to De Morgan's Law, \( (A \cap B)' \) is equivalent to:

A) \( A' \cap B' \)

B) \( A' \cup B' \)

C) \( A \cup B \)

D) \( (A \cup B)' \)

Answer

Correct Answer: B

Mastering Set Theory: The Logic of Collections | Concept of Maths

Mastering Set Theory: The Logic of Collections | Concept of Maths

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5. If \( n(A) = p \) and \( n(B) = q \), what is the maximum number of elements in \( A \cup B \)?

6. Which of the following is an empty set?

7. If \( U = \{1, 2, 3, ..., 10\} \), \( A = \{1, 3, 5, 7, 9\} \), and \( B = \{2, 4, 6, 8, 10\} \), then \( (A \cup B)' \) is:

8. The number of elements in the power set of a power set of an empty set, \( P(P(\emptyset)) \), is:

9. If \( A \subset B \), then \( A - B \) is equal to:

10. In a survey, 70% of people like Tea, 80% like Coffee. What is the minimum percentage of people who like both?

11. If \( A \) and \( B \) are two sets such that \( n(A-B) = 24 \), \( n(B-A) = 19 \) and \( n(A \cap B) = 11 \), find \( n(A \cup B) \).

12. For any two sets \( A \) and \( B \), \( A \cap (A \cup B)' \) is:

13. Let \( A = \{x : x \in \mathbb{N}, x \text{ is a multiple of 3}\} \) and \( B = \{x : x \in \mathbb{N}, x \text{ is a multiple of 5}\} \). Then \( A \cap B \) is:

14. If \( A = \{1, 3, 5\} \) and \( B = \{2, 4\} \), then \( n(P(A \times B)) \) is:

15. Which of the following sets is infinite?

16. If \( A, B, C \) are three sets, then \( A \cap (B - C) \) is equal to:

17. Two finite sets have \( m \) and \( n \) elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of \( m \) and \( n \) are:

18. What is the interval representation of \( \{x : x \in \mathbb{R}, -2 < x \le 5\} \)?

19. If \( n(A) = 10 \), \( n(B) = 15 \), then the minimum number of elements in \( A \cup B \) is:

20. According to De Morgan's Law, \( (A \cap B)' \) is equivalent to:

Interactive Grade 11 Maths Quiz: Sets | Concept of Maths

1. If a set \( A \) has 4 elements, how many non-empty proper subsets does \( A \) have?

2. Given \( A = \{x : x^2 - 5x + 6 = 0\} \) and \( B = \{2, 4\} \). Find \( A \Delta B \) (Symmetric Difference).

3. In a class of 50 students, 30 like Cricket, 25 like Football, and 10 like both. How many like neither?

4. Let \( A = \{1, 2, \{3, 4\}, 5\} \). Which of the following statements is FALSE?

Mastering Set Theory: The Logic of Collections | Concept of Maths

Mastering Set Theory: The Logic of Collections | Concept of Maths

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5. If \( n(A) = p \) and \( n(B) = q \), what is the maximum number of elements in \( A \cup B \)?

6. Which of the following is an empty set?

7. If \( U = \{1, 2, 3, ..., 10\} \), \( A = \{1, 3, 5, 7, 9\} \), and \( B = \{2, 4, 6, 8, 10\} \), then \( (A \cup B)' \) is:

8. The number of elements in the power set of a power set of an empty set, \( P(P(\emptyset)) \), is:

9. If \( A \subset B \), then \( A - B \) is equal to:

10. In a survey, 70% of people like Tea, 80% like Coffee. What is the minimum percentage of people who like both?

11. If \( A \) and \( B \) are two sets such that \( n(A-B) = 24 \), \( n(B-A) = 19 \) and \( n(A \cap B) = 11 \), find \( n(A \cup B) \).

12. For any two sets \( A \) and \( B \), \( A \cap (A \cup B)' \) is:

13. Let \( A = \{x : x \in \mathbb{N}, x \text{ is a multiple of 3}\} \) and \( B = \{x : x \in \mathbb{N}, x \text{ is a multiple of 5}\} \). Then \( A \cap B \) is:

14. If \( A = \{1, 3, 5\} \) and \( B = \{2, 4\} \), then \( n(P(A \times B)) \) is:

15. Which of the following sets is infinite?

16. If \( A, B, C \) are three sets, then \( A \cap (B - C) \) is equal to:

17. Two finite sets have \( m \) and \( n \) elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of \( m \) and \( n \) are:

18. What is the interval representation of \( \{x : x \in \mathbb{R}, -2 < x \le 5\} \)?

19. If \( n(A) = 10 \), \( n(B) = 15 \), then the minimum number of elements in \( A \cup B \) is:

20. According to De Morgan's Law, \( (A \cap B)' \) is equivalent to: