Question

Let $R$ be a relation in $N$ defined by $R=\{(x,y):x+2y=8,x,y\in N\}$. The range of $R$ is

• A. $\{2,4,6\}$
• B. $\{1,2,3\}$
• C. $\{1,2,3,4,6\}$
• D. $\{4,5,6,7\}$

Answer 1

Answer: (B)

$R=\{(x,y):x+2y=8,x,y\in N\}$
$x+2y=8$
$\Rightarrow y=\frac{8-x}{2}$
$x=1$
$\Rightarrow y=\frac{7}{2}\notin N$;
$x=2$
$\Rightarrow y=3\in N$
$x=3$
$\Rightarrow y=\frac{5}{2}\notin N$;
$x=4$
$\Rightarrow y=2\in N$
$x=5$
$\Rightarrow y=\frac{3}{2}\notin N$;
$x=6$
$\Rightarrow y=1\in N$
$x=7$
$\Rightarrow y=\frac{1}{2}\notin N$;
$x=8$
$\Rightarrow y=0\notin N$
$\therefore R=\{(2,3),(4,2),(6,1)\}$
$\therefore$ Range of $R=\{y:(x,y)\in R\}=\{1,2,3\}$