Grade 11 : Mathematics - Sets (Set 3) | Concept of Maths

Question 1

Consider the sets $A = \{x : x \in \mathbb{N}, x < 5\}$ and $B = \{x : x \in \mathbb{Z}, |x| \leq 2\}$. Find the cardinality of the power set of the intersection, $n(P(A \cap B))$.

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 8

Answer

D) 16

Question 2

Let $A$ be the open-closed interval $(-3, 5]$ and $B$ be the closed-open interval $[2, 8)$. Which of the following represents $A \cap B$?

Accepted Answer

B) $[2, 5]$

Answer

A) $(-3, 8)$

Answer

C) $(2, 5)$

Answer

D) $[2, 5)$

Question 3

In a research facility of 100 astronomers, 60 focus on Black Holes, 50 focus on Nebulae, and 20 focus on neither. How many astronomers focus on both Black Holes and Nebulae?

Accepted Answer

D) 30

Answer

A) 10

Answer

B) 20

Answer

C) 40

Question 4

Simplify the set expression: $A \cap (A \cup B)'$.

Accepted Answer

A) $\emptyset$

Answer

B) $A$

Answer

C) $B'$

Answer

D) $A \cap B'$

Question 5

If $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7\}$, find the symmetric difference $A \Delta B$.

Accepted Answer

C) $\{1, 2, 3, 6, 7\}$

Answer

A) $\{4, 5\}$

Answer

B) $\{1, 2, 3, 4, 5, 6, 7\}$

Answer

D) $\{1, 2, 3\}$

Question 6

If $n(A) = 3$, $n(B) = 4$, and the total number of elements in the triple Cartesian product $n(A imes B imes C) = 60$, what is $n(C)$?

Accepted Answer

A) 5

Answer

B) 12

Answer

C) 15

Answer

D) 7

Question 7

Let $X = \{x : x^2 - 5x + 6 = 0\}$ and $Y = \{x : x^2 - 7x + 12 = 0\}$. Find $X \cap Y$.

Accepted Answer

B) $\{3\}$

Answer

A) $\{2\}$

Answer

C) $\{3, 4\}$

Answer

D) $\{2, 3, 4\}$

Question 8

How many subsets does the set $S = \{ \emptyset, \{ \emptyset \} \}$ have?

Accepted Answer

D) 4

Answer

A) 1

Answer

B) 2

Answer

C) 3

Question 9

Identify the nature of the set $A = \{x \in \mathbb{R} : x^2 + 1 = 0\}$.

Accepted Answer

A) Empty Set

Answer

B) Singleton Set

Answer

C) Infinite Set

Answer

D) Universal Set

Question 10

In a shipment of 50 electronic components: 30 are Resistors ($R$), 25 are Inductors ($L$), and 20 are Capacitors ($C$). Known overlaps: $n(R \cap L) = 10, n(L \cap C) = 8, n(R \cap C) = 12$. If 5 components are a combination of all three types, how many components belong to **exactly one** category?

Accepted Answer

B) 30

Answer

A) 25

Answer

C) 15

Answer

D) 35