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MathsClass 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) \(\{1,2\}, \{1,3\}\)

Answer

Answer: A
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 \(\{2,1\}\)
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