Chapter 2 — Relations and Functions

Chapter 2 of the Class 11 Maths NCERT textbook, "Relations and Functions", covers ordered pairs, cartesian products, relations (domain, range, codomain), and special function types. The chapter PDF is free to download.

• From cartesian products to relations — The chapter builds relationships between sets starting from cartesian products of ordered pairs, then defines a relation as a subset of that product — the structure that lets you map how elements of one set connect to another.
• What makes a relation a function — A function is a special relation in which every input has exactly one image, so not every relation qualifies. This distinction is the central idea that separates arbitrary mappings from the well-behaved functions calculus needs.
• Types and algebra of functions — It surveys real-valued functions — polynomial, rational, modulus, signum, greatest-integer and more — and shows how functions can themselves be added, subtracted, multiplied and divided to build new functions.

1. 01Cartesian product P × Q = {(p,q) : p ∈ P, q ∈ Q}; equals empty set if either set is empty
2. 02Ordered pairs are equal only if both corresponding elements match: (a,b) = (x,y) iff a=x and b=y
3. 03Relation R from set A to B is a subset of A × B; domain = first elements, range = second elements, codomain = entire set B
4. 04Function f: A → B requires every element of A to have exactly one image in B; not all relations are functions
5. 05Real function has domain and range as R or subsets of R; common types include polynomial, rational, modulus, and signum functions
6. 06Algebra of functions: (f±g)(x) = f(x)±g(x), (fg)(x) = f(x)g(x), (f/g)(x) = f(x)/g(x) where g(x)≠0