Question 1

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

A) 16B) 15C) 14D) 13

Answer

✓ Correct Answer: Option 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: Option A

Question 3

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: Option 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 + qB) \max(p, q)C) $p \times q$D) $p^q$

Answer

✓ Correct Answer: Option 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: Option 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) UB) \emptysetC) \{1, 2, ..., 10\}D) \{5, 6\}

Answer

✓ Correct Answer: Option 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) 0B) 1C) 2D) 4

Answer

✓ Correct Answer: Option C

Question 9

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

A) AB) BC) \emptysetD) B - A

Answer

✓ Correct Answer: Option 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: Option 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) 43B) 54C) 35D) 65

Answer

✓ Correct Answer: Option B

Question 12

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

A) AB) BC) \emptysetD) $A \cap B$

Answer

✓ Correct Answer: Option C

Question 13

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

A) Multiples of 8B) Multiples of 15C) Multiples of 2D) Empty Set

Answer

✓ Correct Answer: Option B

Question 14

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

A) 32B) 64C) 8D) 128

Answer

✓ Correct Answer: Option B

Question 15

15. Which of the following sets is infinite?

A) $\{x \in \mathbb{Z} : -100 < x < 100\}$B) $\{x \in \mathbb{N} : x is prime\}$C) The set of months in a yearD) $\{x \in \mathbb{R} : x^2 - 4 = 0\}$

Answer

✓ Correct Answer: Option 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: Option 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, 6B) 6, 3C) 5, 1D) 8, 7

Answer

✓ Correct Answer: Option 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: Option C

Question 19

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

A) 10B) 15C) 25D) 5

Answer

✓ Correct Answer: Option 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: Option B

Accepted Answer

✓ Correct Answer: Option A

Interactive Grade 11 Maths Quiz: Sets

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?

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 $A = \{x : x \in \mathbb{N}, x is a multiple of 3\}$ and $B = \{x : x \in \mathbb{N}, x is a multiple of 5\}$. 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: