Grade 11 : Mathematics - Relations (Set 5) | Concept of Maths

Question 1

If set $A = \{x : x \in \mathbb{N}, x < 3\}$ and B = \{3, 4, 5\}, what is the total number of elements in the triple Cartesian product $A 	imes B 	imes A$?

Accepted Answer

C) 12

Answer

A) 6

Answer

B) 9

Answer

D) 18

Question 2

A relation R is defined on the set of whole numbers $\mathbb{W}$ by R = \{(x, y) : 2x + 3y = 12\}. Which of the following represents the Range of R?

Accepted Answer

B) \{0, 2, 4\}

Answer

A) \{0, 2, 4, 6\}

Answer

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

Answer

D) \{0, 3, 6\}

Question 3

Consider the relation $R = \{(x, y) : y = x + \frac{4}{x}, x \in \{1, 2, 4\}, y \in \mathbb{N}\}$. What is the inverse relation $R^{-1}$?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

Let A = \{a, b, c\} and B = \{1, 2\}. How many non-empty relations can be defined from A to B?

Accepted Answer

A) 63

Answer

B) 64

Answer

C) 31

Answer

D) 32

Question 5

In a digital network, signals are sent from a set of transmitters T = \{2, 3, 5\} to receivers R = \{10, 15, 20, 25\}. A relation S is established such that t S r if and only if t is a factor of r. How many ordered pairs are in S?

Accepted Answer

C) 7

Answer

A) 5

Answer

B) 6

Answer

D) 8

Question 6

A relation R is defined on the set of integers $\mathbb{Z}$ by $aRb ⇔ a^2 = b^2$. Which of the following is true?

Accepted Answer

B) R = \{(a, b) : a = b  or  a = -b\}

Answer

A) R = \{(a, b) : a = b\}

Answer

C) R only contains positive integers

Answer

D) R is an empty relation

Question 7

Determine the domain of the relation $R = \{(x, y) : y = \sqrt{16 - x^2}, x \in \mathbb{Z}, y \in \mathbb{R}\}$.

Accepted Answer

A) \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}

Answer

B) \{0, 1, 2, 3, 4\}

Answer

C) \{-4, 4\}

Answer

D) $\{x : -4 \le x \le 4, x \in \mathbb{R}\}$

Question 8

Let A = \{1, 2, 3, 4, 5\}. A relation R on A is defined as R = \{(x, y) : x < y\}. How many elements are in the set R?

Accepted Answer

D) 10

Answer

A) 5

Answer

B) 25

Answer

C) 15

Question 9

If R is a relation from A = \{1, 2, 3\} to B = \{4, 5\} defined by R = \{(1, 4), (2, 4), (3, 5)\}, then the Range of R is:

Accepted Answer

C) \{4, 5\}

Answer

A) \{1, 2, 3\}

Answer

B) \{4\}

Answer

D) \{5\}

Question 10

An identity relation $I_A$ on set A = \{p, q, r\} is defined as:

Accepted Answer

B) \{(p, p), (q, q), (r, r)\}

Answer

A) \{(p, p), (q, q)\}

Answer

C) \{(p, q), (q, r), (r, p)\}

Answer

D) \{(p, p), (q, q), (r, r), (p, q)\}