Question

The domain and range of relation $R=\left\{\right(x,y)|x,y\in N$, $x+2y=5\}$ is?

• A. $\{1,3\},\{2,1\}$
• B. $\{2,1\},\{3,2\}$
• C. $\{1,3\},\{1,1\}$
• D. $\{1,2\},\{1,3\}$

Answer 1

The correct option is A $\{1,3\},\{2,1\}$

The possible values of $x$ which satisfies the given relation is the domain of the relation

The possible values of $y$ which satisfies the given relation is the range of the relation

Given that $x,y$ are natural numbers and the relation is $x+2y=5$

For $x=1$ , the value of $y$ is $2$

For $x=3$ , the value of $y$ is $1$

If $x\ge 5$, then $y$ is negative which does not belong to naturals.

If $x=2,4$ then $y$ becomes rational number which is not in naturals.

Thus, only $1$ and $3$ gives $y$ as natural numbers $2$ and $1$.

Therefore, the domain is $\{1,3\}$ and the range is $\{2,1\}$