Grade 11 : Mathematics - Relations (Set 4) | Concept of Maths

Question 1

Imagine a coordinate plane where set A = \{1, 2\} is represented on the x-axis and set B = \{3, 4\} is represented on the y-axis. If we plot every point of the Cartesian product $A \times B$, how many distinct points will be visible on the grid?

Accepted Answer

C) 4 points

Answer

A) 2 points

Answer

B) 3 points

Answer

D) 8 points

Question 2

A mapping diagram shows arrows from set X = \{a, b\} to set Y = \{1, 2, 3\}. If an arrow goes from a to 1 and another arrow goes from b to 1, which of the following represents this relation R?

Accepted Answer

A) R = \{(a, 1), (b, 1)\}

Answer

B) R = \{(1, a), (1, b)\}

Answer

C) R = \{(a, b), (1, 1)\}

Answer

D) R = \{(a, 1), (b, 2)\}

Question 3

Consider a relation R plotted on a grid as points (2, 4), (3, 9), and (4, 16). What is the Range of this relation if we view it as a set of outputs?

Accepted Answer

B) \{4, 9, 16\}

Answer

A) \{2, 3, 4\}

Answer

C) \{2, 4, 3, 9, 4, 16\}

Answer

D) $\{x, y : y = x^2\}$

Question 4

Suppose set A has 2 elements and set B has 1 element. If you visualize all possible subsets of $A \times B$ as different possible graphs, how many such graphs (relations) can you create?

Accepted Answer

D) 4

Answer

A) 2

Answer

B) 3

Answer

C) 1

Question 5

On a $3 \times 3$ grid where $x, y \in \{1, 2, 3\}$, a relation R is defined by the condition x = y. How do the points of this relation appear visually?

Accepted Answer

B) A diagonal line from (1, 1) to (3, 3)

Answer

A) A horizontal line at y=1

Answer

C) A vertical line at x=2

Answer

D) Points at the four corners of the grid

Question 6

If a relation R is represented by points on a coordinate plane, and we reflect all those points across the line y = x, which new relation have we visually constructed?

Accepted Answer

A) The inverse relation $R^{-1}$

Answer

B) The complement relation R'

Answer

C) The identity relation I

Answer

D) The universal relation $A \times A$

Question 7

In an arrow diagram from A = \{10, 20\} to B = \{5, 15\}, an arrow is drawn only if x > y. Which ordered pairs are in this relation?

Accepted Answer

C) \{(10, 5), (20, 5), (20, 15)\}

Answer

A) \{(10, 15), (20, 5)\}

Answer

B) \{(10, 5), (10, 15), (20, 15)\}

Answer

D) \{(5, 10), (15, 20)\}

Question 8

A graph shows no points plotted even though the sets A and B are non-empty. Which mathematical relation does this visual represent?

Accepted Answer

D) Empty Relation

Answer

A) Identity Relation

Answer

B) Universal Relation

Answer

C) Reflexive Relation

Question 9

If A = \{1, 2, 3\} and a relation R on A is represented by the points (1,1), (2,2), (3,3), what is the Domain?

Accepted Answer

B) \{1, 2, 3\}

Answer

A) \{1, 2\}

Answer

C) \{3, 2, 1, 0\}

Answer

D) \phi\

Question 10

Visualizing the Cartesian product $A \times A$ where A = \{p, q\}. If we draw this as a table, how many cells will the table have?

Accepted Answer

C) 4

Answer

A) 2

Answer

B) 3

Answer

D) 1