Grade 11 : Mathematics - Sets (Set 1) | Concept of Maths

Question 1

1. If a set \( A \) has 3 elements, how many elements are there in the power set of the power set of \( A \), denoted by \( n(P(P(A))) \)?

A) 64

B) 128

C) 256

D) 512

Answer

Correct Answer: C

Question 2

2. For any two sets \( A \) and \( B \), the set \( (A \cup B)' \cup (A' \cap B) \) is equal to:

A) \( A \)

B) \( A' \)

C) \( B' \)

D) \( \phi \)

Answer

Correct Answer: B

Question 3

3. In a class of 50 students, 35 like Mathematics and 25 like Statistics. If each student likes at least one of the two subjects, how many students like both Mathematics and Statistics?

A) 10

B) 15

C) 20

D) 5

Answer

Correct Answer: A

Question 4

4. Let \( A = \{x : x^2 - 5x + 6 = 0\} \) and \( B = \{x : x^2 - 3x + 2 = 0\} \). What is the symmetric difference \( A \Delta B \)?

A) \( \{1, 2, 3\} \)

B) \( \{2\} \)

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

D) \( \{1, 3\} \)

Question 5

5. If \( A \) and \( B \) are two sets such that \( n(A) = 15 \), \( n(B) = 20 \), and \( n(A \cap B) = 5 \), find the value of \( n(A \Delta B) \).

A) 30

B) 35

C) 25

D) 20

Answer

Correct Answer: C

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) \( \{x : x \in \mathbb{R}, x^2 - 9 = 0\} \)

D) \( \{0\} \)

Answer

Correct Answer: B

Question 7

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

A) \( B' \)

B) \( \{1, 2, 5, 6, 7\} \)

C) \( \phi \)

D) \( \{1, 2, 5\} \)

Answer

Correct Answer: D

Question 8

8. If \( A \subset B \), then which of the following statements is always TRUE?

A) \( A \cup B = B \)

B) \( A \cap B = B \)

C) \( A - B = A \)

D) \( B \subset A \)

Answer

Correct Answer: A

Question 9

9. The set \( A = \{x : x \text{ is a positive prime number less than 10}\} \) in roster form is:

A) \( \{1, 2, 3, 5, 7\} \)

B) \( \{2, 3, 5, 7\} \)

C) \( \{3, 5, 7, 9\} \)

D) \( \{2, 4, 6, 8\} \)

Answer

Correct Answer: B

Question 10

10. If \( A \) and \( B \) are finite sets such that \( n(A-B) = 18 \), \( n(B-A) = 25 \) and \( n(A \cap B) = 12 \), find \( n(A \cup B) \).

A) 43

B) 30

C) 55

D) 67

Answer

Correct Answer: C

Grade 11 : Mathematics - Sets (Set 1) | Concept of Maths