The figure shows a relation between the sets $P$ and $Q$. Write this relation in set-builder form. What are its domain and range?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) From the figure,we observe the following mappings:
$9$ $\rightarrow 3, 9$ $\rightarrow -3$
$4$ $\rightarrow 2, 4$ $\rightarrow -2$
$25$ $\rightarrow 5, 25$ $\rightarrow -5$
This indicates that each element $x$ in set $P$ is the square of the corresponding element $y$ in set $Q$.
$1.$ Set-builder form:
$R = \{(x, y) : x = y^2, x \in P, y \in Q\}$
$2.$ Domain:
The set of all first elements of the ordered pairs in $R$ is $\{4, 9, 25\}$.
$3.$ Range:
The set of all second elements of the ordered pairs in $R$ is $\{-5, -3, -2, 2, 3, 5\}$.

Explore More

Similar Questions

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

Relation $R$ on set $N$ is defined as follows:
$R = \{(a, b) : a = b - 2, b > 6\}$. Select the appropriate option.

If $A = \{1, 2, 3\}$ and $B = \{1, 4, 6, 9\}$,and $R$ is a relation from $A$ to $B$ defined by "$x$ is greater than $y$",then the range of $R$ is:

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo