1. **Problem Statement:** Define and give examples of (i) one-to-one function, (ii) onto function, and (iii) bijection between non-empty sets $X$ and $Y$. 2. **Definitions and Examples:** (i) **One-to-one function (Injective):** A function $f:X \to Y$ is one-to-one if different elements in $X$ map to different elements in $Y$. Formally, if $f(x_1) = f(x_2)$ implies $x_1 = x_2$. *Example:* Let $X = \{1,2,3\}$ and $Y = \{a,b,c,d\}$. Define $f$ by $f(1)=a$, $f(2)=b$, $f(3)=c$. Here, no two elements in $X$ map to the same element in $Y$, so $f$ is one-to-one. (ii) **Onto function (Surjective):** A function $f:X \to Y$ is onto if every element in $Y$ has at least one pre-image in $X$. Formally, for every $y \in Y$, there exists $x \in X$ such that $f(x) = y$. *Example:* Let $X = \{1,2,3\}$ and $Y = \{a,b,c\}$. Define $f$ by $f(1)=a$, $f(2)=b$, $f(3)=c$. Every element of $Y$ is covered, so $f$ is onto. (iii) **Bijection:** A function $f:X \to Y$ is a bijection if it is both one-to-one and onto. This means each element of $X$ maps to a unique element of $Y$, and all elements of $Y$ are covered. *Example:* Using the same sets and function as in (ii), $f$ is both one-to-one and onto, so it is a bijection. 3. **Summary:** - One-to-one means no two inputs share the same output. - Onto means every output is covered by some input. - Bijection means both conditions hold simultaneously. Final answer: Definitions and examples as above.