If R = { ( x , y ) : x + 2 y = 8 } is a relation on N , then the range of R is:

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. {1, 2, 3}

Explanation:

The given relation on $N$ is $R = {(x, y) : x + 2 y = 8}$

Since both $x, y \in N$ ,

$x$ can take the values (2, 4, 6) for all $x, y \in N$

For $x = 2$ , $2 + 2 y = 8$

$\Rightarrow$ $y = 3$

For $x = 4$ , $4 + 2 y = 8$

$\Rightarrow$ $y = 2$

For $x = 6$ , $6 + 2 y = 8$

$\Rightarrow$ $y = 1$

Hence, $R = {(2, 3), (4, 2), (6, 1)}$

Range of $R$ = Set of second elements $= {1, 2, 3}$

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