Let $A =$ { $1, 2, 3, 4, . . . 14$ }. Define a relation $R$ from $A$ to $A$ by $R =$ { $(x, y) : 3 x - y = 0, where x, y ϵ A$ }. Write down its domain, co-domain, and range.

Open in App

Solution

Given
$A =$ { $1, 2, 3, 4, . . . 14$ }
$R$ is relation from $A$ to $A$
$R =$ { $(x, y) : 3 x - y = 0, where x, y ϵ A$ }

Find relation from $A$ to $A$ in roster form
$R =$ { $(x, y) : 3 x - y = 0, where x, y ϵ A$ }
Put $x = 1, 2, 3, 4$ we get,
$y = 3, 6, 9, 12$ respectively
So, $R =$ { $(1, 3), (2, 6), (3, 9), (4, 12)$ }

Domain of $R$
The domain of $R$ is the set of all first elements of ordered pairs in relation $R$ ,
Hence, domain of $R =$ { $1, 2, 3, 4$ }

Co-domain of $R$
If a relation is defined from $P \to Q$ , then whole set $Q$ is the co-domain of that relation.
Hence, co-domain of $R = A =$ { $1, 2, 3, . . . 14$ }

Range of $R$
The range of $R$ is set of second elements of ordered pairs in relation $R$ .
Hence, range of $R$ is { $3, 6, 9, 12$ }.

Suggest Corrections

Similar questions

Q. Let

A = {1, 2, 3, . . . ., 14}

. Define a relation

R

from

A

A

R = {(x, y) : 3 x - y = 0

where

x, y \in A}

. Write down its domain, co-domain and range.

Let A = {1, 2, 3,....., 14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where $x, y ϵ A$ } Write down its domain, codomain and range.

Q. Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = { ( x , y ): 3 x – y = 0, where x , y ∈ A}. Write down its domain, codomain and range.

Let A = {1, 2, 3,.....,14}. Define a relation on a set A by

R = {(x, y) : 3x - y = 0, where $x, y ϵ A$ }.

Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

Q. Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(x, y) : 3x − y = 0, where x, y ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

Join BYJU'S Learning Program

Explore more

Cartesian Product

Standard XII Mathematics

Join BYJU'S Learning Program

Let A= {1,2,3,4,...14}. Define a relation R from A to A by R= {(x,y):3x−y=0,where x,y ϵ A}. Write down its domain, co-domain, and range.

Let $A =$ { $1, 2, 3, 4, . . . 14$ }. Define a relation $R$ from $A$ to $A$ by $R =$ { $(x, y) : 3 x - y = 0, where x, y ϵ A$ }. Write down its domain, co-domain, and range.