Grade 11 : Mathematics - Relations (Set 9) | Concept of Maths

Question 1

Let $A = \{x \in \mathbb{Z} : |x| \leq 2\}$ and B = \{1, 2, 3\}. Find the number of elements in the intersection of the Cartesian products $(A 	imes B) \cap (B 	imes A)$.

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 6

Answer

D) 9

Question 2

In a database of prime numbers, a relation R is defined on the set S = \{11, 13, 17, 19, 23, 29, 31\} such that xRy if and only if |x - y| = 2 (Twin Primes). Find the number of elements in R.

Accepted Answer

B) 6

Answer

A) 3

Answer

C) 4

Answer

D) 2

Question 3

Let A = \{1, 2, 3, 4, 5\}. A relation R is defined on A as $R = \{(x, y) : |x^2 - y^2| < 9\}$. What is the total number of elements in R?

Accepted Answer

A) 13

Answer

B) 11

Answer

C) 15

Answer

D) 25

Question 4

Let $R = \{(x, y) : x, y \in \mathbb{W}, x^2 + y^2 = 25\}$, where $\mathbb{W}$ is the set of whole numbers. Find the domain of the inverse relation $R^{-1}$.

Accepted Answer

D) \{0, 3, 4, 5\}

Answer

A) \{0, 3, 4, 5, 6\}

Answer

B) \{3, 4, 5\}

Answer

C) \{0, 5\}

Question 5

A set A has 3 elements. How many relations can be defined on A that contain the specific element (1, 1)?

Accepted Answer

B) $2^8$

Answer

A) $2^9$

Answer

C) $2^3$

Answer

D) $2^7$

Question 6

Let R be a relation on $\mathbb{N}$ defined by xRy ⇔ 2x + 5y = 40. The range of R is:

Accepted Answer

C) \{2, 4, 6, 7\}

Answer

A) \{2, 4, 6\}

Answer

B) \{5, 10, 15\}

Answer

D) \{2, 4, 6\} (Wait, let's calculate properly)

Question 7

Let A = \{a, b, c\}. What is the total number of reflexive relations that can be formed on A?

Accepted Answer

B) 64

Answer

A) $2^9$

Answer

C) 512

Answer

D) $2^3$

Question 8

If n(A) = 4 and n(B) = 3, find the number of non-empty relations from A to B.

Accepted Answer

A) 4095

Answer

B) 4096

Answer

C) 12

Answer

D) $2^{12}$

Question 9

Let $R = \{(x, y) : x, y \in \mathbb{Z}, x^2 + 3y^2 \leq 12\}$. How many elements are in the domain of R?

Accepted Answer

C) 7

Answer

A) 5

Answer

B) 6

Answer

D) 9

Question 10

Let A = \{1, 2, 3\} and B = \{a, b\}. Let R be a relation from A to B defined by R = \{(1, a), (1, b), (2, a), (3, b)\}. Find $R^{-1}$.

Accepted Answer

D) \{(a, 1), (b, 1), (a, 2), (b, 3)\}

Answer

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

Answer

B) \{(1, a), (2, a), (3, b)\}

Answer

C) \{(a, 1), (a, 2), (b, 3)\}