# If $R = \{ (x, y) : x + 2y =8\}$ is a relation on N. write the range of R

$(a)\;{1,0,3}\qquad(b)\;{1 , 2, 3}\qquad(c)\;{{4,2,1}}\qquad(d)\;{5,4,7}$

Given $R = \{ (x,y) : x+2y=8 \}$
Given that the relation is on N
$y = 8-\large\frac{x}{2}$
When x=1, y = $\large\frac{7}{2}$ which is not
When $x=2, y=3$
When $x=3, y=\large\frac{7}{2}$ which is not
When $x=4, y=2$
When $x=5, y=\large\frac{3}{2}$ which is not
When $x=6, y=1$
$\therefore (2,3), (4,2), (6,1)$
Hence the range is $\{ 1,2,3 \}$