Chapter 2 — Relations and Functions

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

Chapter 2 introduces the concept of relations and functions—fundamental mathematical structures for mapping relationships between sets. The chapter begins with cartesian products (ordered pairs from two sets) and explains the formula that if n(A) = p and n(B) = q, then n(A × B) = pq. Relations are subsets of cartesian products with defined domain, range, and codomain. Functions are special relations where every element in the domain has exactly one image. The chapter covers real-valued and real functions, algebra of functions (addition, subtraction, multiplication, quotient), and various function types: identity, constant, polynomial, rational, modulus, signum, and greatest integer 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