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QuestionMathsClass 12

The domain and range of relation $$R=\{(x,y) | x, y \in N$$, $$x+2y=5\}$$ is?
(A) $$\{1,3\}, \{2,1\}$$
(B) $$\{2,1\}, \{3,2\}$$
(C) $$\{1,3\}, \{1,1\}$$
(D) $$\{1,2\}, \{1,3\}$$

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 $$x\geq 5$$, 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 $$\{2,1\}$$