Sets, Relations and Functions

Board: JEE Class: JEE

Chapter Overview

Sets, operations, Venn diagrams. Relations: reflexive, symmetric, transitive, equivalence classes. Functions: domain, range, one-to-one, onto, bijective, composition, inverses. Real-valued functions and their properties. JEE-specific problem types include function parity, periodicity, and functional equations.

Topics Covered

Set Theory and Operations
Relations and Properties
Equivalence Relations
Functions and Mappings
Domain and Range
Composite Functions
Functional Equations
Periodic Functions

Key Formulas

n(AUB) = n(A)+n(B)-n(AnB)

f o g defined when range(g) subset domain(f)

Periodic: f(x+T) = f(x)

Real-World Applications

Applications: JEE problem solving, mathematical logic foundations.

Study Tips

Tip: Solve JEE previous year questions

Tip: Focus on tricky domain problems

Tip: Practice functional equations