Question

13. If R = {x, y)/x = 2y} is a relation defined on A = {1, 2, 3, 4, 6, 7, 8} then write all elements of R Also
write its Domain and Range?

Answer 1

$\textbf{Given:}$

$A=\{1,2,3,4,6,7,8\}$

$\textbf{To find:}$

$\text{Elements of R, domain and range}$

$\textbf{Solution:}$

$x=2y\implies\,y=\dfrac{x}{2}$

$\text{when x=2,}\,y=\dfrac{2}{2}=1$

$\implies\,(2,1)\,\in\,R$

$\text{when x=4,}\,y=\dfrac{4}{2}=2$

$\implies\,(4,2)\,\in\,R$

$\text{when x=6,}\,y=\dfrac{6}{2}=3$

$\implies\,(6,3)\,\in\,R$

$\text{when x=8,}\,y=\dfrac{8}{2}=4$

$\implies\,(8,4)\,\in\,R$

$\therefore\bf\,R=\{(2,1),(4,2),(6,3),(8,4)\}$

$\textbf{Domain}=\{2,4,6,8\}$

$\textbf{Range}=\{1,2,3,4\}$