Question

M={1,2,3,4,5,6,7,8,9,10} define a relation R from M to M by R={(x,y):x+y=6; where x and y E M} write down its domain codomain and rangeM={1,2,3,4,5,6,7,8,9,10} define a relation R from M to M by R={(x,y):x+y=6; where x and y E M} write down its domain codomain and range​

Answer 1

$\textbf{Given:}$

$M=\{1,2,3,4,5,6,7,8,9,10\}\;\text{and}$

$R=\{(x,y):\;x+y=6\;x,y\,{\in}\,M\}$

$\textbf{To find:}$

$\text{Domain and range of R}$

$\textbf{Solution:}$

$1+5=6\;\implies\;(1,5),(5,1)\,\in\,R$

$2+4=6\;\implies\;(2,4),(4,2)\,\in\,R$

$3+3=6\;\implies\;(3,3)\,\in\,R$

$\therefore\bf\,R=\{(1,5),(5,1),(2,4),(4,2),(3,3)\}$

$\textbf{Domain of R}\bf=\{1,2,3,4,5\}$

$\textbf{Range of R}\bf=\{1,2,3,4,5\}$