Grade 11 : Mathematics - Sets (Set 2) | Concept of Maths

Question 1

1. 1. Let \( A = \{x : x \text{ is a divisor of } 18\} \) and \( B = \{x : x \text{ is a divisor of } 24\} \). Find the number of elements in \( A \cap B \).

A) 2

B) 3

C) 4

D) 6

Answer

Correct Answer: C

Question 2

2. 2. If a set \( S \) has \( n \) elements, then the number of non-empty proper subsets of \( S \) is:

A) \( 2^n - 1 \)

B) \( 2^n - 2 \)

C) \( 2^{n-1} \)

D) \( 2^n \)

Answer

Correct Answer: B

Hint: A proper subset cannot be the set itself, and a non-empty set cannot be \(\emptyset\).

Question 3

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

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

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

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

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

Answer

Correct Answer: A

Question 4

4. 4. Given \( U = \{1, 2, 3, \dots, 10\} \), \( A = \{1, 3, 5, 7, 9\} \), and \( B = \{2, 3, 5, 7\} \). Find \( (A \cup B)' \).

A) \( \{4, 6, 8\} \)

B) \( \{2, 4, 6, 8, 10\} \)

C) \( \{1, 2, 3, 5, 7, 9\} \)

D) \( \{4, 6, 8, 10\} \)

Question 5

5. 5. In a survey of 100 students, 60 like Mathematics, 45 like Physics, and 20 like both. How many students like neither Mathematics nor Physics?

A) 5

B) 10

C) 15

D) 25

Answer

Correct Answer: C

Question 6

6. 6. Let \( A = \{x \in \mathbb{R} : 0 < x < 3\} \) and \( B = \{x \in \mathbb{R} : 2 \leq x < 5\} \). What is \( A - B \)?

A) \( (0, 2] \)

B) \( (0, 2) \)

C) \( [2, 3) \)

D) \( (3, 5) \)

Answer

Correct Answer: B

Hint: \( A - B \) contains elements in \( A \) that are NOT in \( B \). Check the boundary at \( x=2 \).

Question 7

7. 7. If \( A \) and \( B \) are two sets such that \( A \subset B \), then which of the following is always true?

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

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

C) \( A - B = B \)

D) \( A \cap B = \emptyset \)

Answer

Correct Answer: A

Question 8

8. 8. Let \( P(A) \) denote the power set of \( A \). If \( A = \emptyset \), then the number of elements in \( P(P(P(A))) \) is:

A) 1

B) 2

C) 3

D) 4

Answer

Correct Answer: D

Question 9

9. 9. The symmetric difference of sets \( A = \{1, 2, 3\} \) and \( B = \{3, 4, 5\} \), denoted by \( A \Delta B \), is:

A) \( \{3\} \)

B) \( \{1, 2, 4, 5\} \)

C) \( \{1, 2, 3, 4, 5\} \)

D) \( \emptyset \)

Answer

Correct Answer: B

Question 10

10. 10. If \( A \) and \( B \) are finite sets such that \( n(A-B) = 25 \), \( n(B-A) = 15 \), and \( n(A \cap B) = 10 \), find \( n(A \cup B) \).

A) 40

B) 45

C) 50

D) 60

Answer

Correct Answer: C

Accepted Answer

Correct Answer: D

Grade 11 : Mathematics - Sets (Set 2) | Concept of Maths