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 $R = \{y: (x, y) \in R\} = \{1,2,3\}$