Appeared in: 2026 (2 sets)
(a) Let $A = \mathbb{R} - \{3\}$ and $B = \mathbb{R} - \{1\}$. A function $f : A \rightarrow B$ is defined by $f(x) = \left$ \frac{x - 2}{x - 3} \right$$. Find whether $f$ is one-one and onto.
OR
(b) Let $n$ be a fixed positive integer. A relation $R$ is defined in set $Z$ such that $R = \{(x, y) : (x - y) \text{ is divisible by } n, x, y \in Z\}$. Determine if $R$ is an equivalence relation.