Relations and Functions

Board: CBSE Class: 12

Chapter Overview

Relations are subsets of A x B with properties: reflexive (aRa for all a), symmetric (if aRb then bRa), transitive (if aRb and bRc then aRc). Equivalence relations satisfy all three. Functions cover injective, surjective, bijective, composition fog(x) = f(g(x)), and inverse functions f^-1(x). Binary operations on sets are introduced.

Topics Covered

Types of Relations
Reflexive-Symmetric-Transitive
Equivalence Relations
Functions Review
Composition of Functions
Inverse Functions
Binary Operations

Key Formulas

(f o g)(x) = f(g(x))

(f o (g o h)) = ((f o g) o h)

f^-1(y) = x iff f(x) = y

Real-World Applications

Applications: Database schema relationships, programming function composition, equivalence classes in modular arithmetic.

Study Tips

Tip: Understand properties through examples

Tip: Practice composition with non-trivial functions

Tip: Verify invertibility conditions