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

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

📚 View Syllabus & Question Overview (10 Questions with Explanations)

Grade 11 : Mathematics - Sets (Set 2)

Interactive Grade 11 Mathematics quiz on Sets. Includes 10 medium-difficulty questions on operations, cardinality, and Venn diagrams.

1. <b>1. Let A = \{x : x is a divisor of 18\} and B = \{x : x is a divisor of 24\}. Find the number of elements in $A \cap B$.</b>

A) 2B) 3C) 4D) 6

✓ Correct Answer: Option C

Explanation: Hint: List divisors of 18 and 24, then find common elements.

2. <b>2. If a set S has n elements, then the number of non-empty proper subsets of S is:</b>

A) $2^n - 1$B) $2^n - 2$C) $2^{n-1}$D) $2^n$

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

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

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✓ Correct Answer: Option B

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

3. <b>3. Let A = \{1, 2, \{3, 4\}, 5\}. Which of the following statements is INCORRECT?</b>

A) $\{3, 4\} \subset A$B) $\{3, 4\} \in A$C) $\{\{3, 4\}\} \subset A$D) $\{1, 2, 5\} \subset A$

✓ Correct Answer: Option A

Explanation: Hint: Check if the element inside the set braces is actually a member of A.

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

A) \{4, 6, 8\}B) \{2, 4, 6, 8, 10\}C) \{1, 2, 3, 5, 7, 9\}D) \{4, 6, 8, 10\}

✓ Correct Answer: Option D

Explanation: Hint: First find $A \cup B$, then find its complement in U.

5. <b>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?</b>

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

✓ Correct Answer: Option C

Explanation: Hint: Use the formula $n(M \cup P) = n(M) + n(P) - n(M \cap P)$.

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

A) (0, 2]B) (0, 2)C) [2, 3)D) (3, 5)

✓ Correct Answer: Option B

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

7. <b>7. If A and B are two sets such that $A \subset B$, then which of the following is always true?</b>

A) $A \cap B = A$B) $A \cup B = A$C) A - B = BD) $A \cap B = \emptyset$

✓ Correct Answer: Option A

Explanation: Hint: If every element of A is in B, what is their intersection?

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

A) 1B) 2C) 3D) 4

✓ Correct Answer: Option D

Explanation: Hint: n(A)=0. Find n(P(A)), then n(P(P(A))), then the next level.

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

A) \{3\}B) \{1, 2, 4, 5\}C) \{1, 2, 3, 4, 5\}D) \emptyset

✓ Correct Answer: Option B

Explanation: Hint: $A \Delta B = (A-B) \cup (B-A)$.

10. <b>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 $n(A \cup B)$.</b>

A) 40B) 45C) 50D) 60

✓ Correct Answer: Option C

Explanation: Hint: $n(A \cup B) = n(A-B) + n(B-A) + n(A \cap B)$.