Question

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

• A. $\{2,4,6\}$
• B. $\{1,2,3\}$
• C. $\{1,2,3,4,5,6\}$
• D. None of these

Answer 1

Answer: (B)

$\{1,2,3\}$

$R=\left\{\right(x,y):x+2y=8,x,yϵN\}$
$x+2y=8\Rightarrow y=\frac{8-x}{2}$
$x=1\Rightarrow y=\frac{7}{2}\text{/}ϵN;x=4\Rightarrow y=2ϵN$

$x=2\Rightarrow y=3;x=5\Rightarrow y=\frac{3}{2}\text{/}ϵN$
$x=3\Rightarrow y=\frac{5}{2}\text{/}ϵN;x=6\Rightarrow y=1\text{/}ϵN$
$x=7\Rightarrow y=\frac{1}{2}\text{/}ϵN;x=8\Rightarrow y=0\text{/}ϵN$
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$\therefore R=\left\{\right(2,3),(4,2),(6,1\left)\right\}$
$\therefore$ Range of $R=\{y:(x,y\left)ϵR\right\}=\{1,2,3\}$.
$\therefore$ the correct answer is B.