(a) A student wants to pair up natural numbers in such a way that they satisfy the equation $2x + y = 41$, $x, y \in \text{N}$. Find the domain and range of the relation. Check if the relation thus formed is reflexive, symmetric and transitive. Hence, state whether it is an equivalence relation or not. OR (b) Show that the function $f : \text{N} \to \text{N}$, where $\text{N}$ is a set of natural numbers, given by $f(n) = \begin{cases} n - 1, \text{ if } n \text{ is even} \\ n + 1, \text{ if } n \text{ is odd} \end{cases}$$ is a bijection.

Year	Paper Code	Set	Position
CBSE 2025	Series 65-6	Set 1	Question 28
CBSE 2025	Series 65-6	Set 2	Question 30
CBSE 2025	Series 65-6	Set 3	Question 29

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)