WBJEE · Maths · Functions
Let \(\rho\) be a relation defined on set of natural numbers \(\mathbb{N}\), as \(\rho=\{(x, y) \in \mathbb{N} \times \mathbb{N}: 2 x+y=41\}\). Then domain \(A\) and range B are
- A \(\mathrm{A} \subset\{\mathrm{x} \in \mathbb{N}: 1 \leq \mathrm{x} \leq 20\}\) and \(B \subset\{\mathrm{y} \in \mathbb{N}: 1 \leq \mathrm{y} \leq 39\}\)
- B \(A=\{x \in \mathbb{N}: 1 \leq x \leq 15\}\) and \(B=\{y \in \mathbb{N}: 2 \leq \mathrm{y} \leq 30\}\)
- C \(\mathrm{A} \equiv \mathbb{N}, \mathrm{B} \equiv \mathbb{Q}\)
- D \(A \equiv \mathbb{Q}, B \equiv \mathbb{Q}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{A} \subset\{\mathrm{x} \in \mathbb{N}: 1 \leq \mathrm{x} \leq 20\}\) and \(B \subset\{\mathrm{y} \in \mathbb{N}: 1 \leq \mathrm{y} \leq 39\}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text {Hint: } & 2 x +y=41 \\ & y=41-2 x \\ \therefore & x=\{1,2,3,4, \ldots .20\} \\ & y=\{1,3,5, \ldots .39\} \end{aligned}\)
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