Sets, Relations and Functions - Part 1

Following are the topics which we'll be covering in series of sessions. We will also discuss some key concepts to be covered from JEE perspective. I am going to do this for other chatpers as well

1. Sets

Definition of a Set and Different Types of Sets

Finite and Infinite Sets

Empty (Null) Set

Equal Sets

Subsets, Power Set, and Universal Set

Operations on Sets

Union of Sets (A ∪ B)

Intersection of Sets (A ∩ B)

Difference of Sets (A - B)

Complement of a Set

Venn Diagrams

Properties of Set Operations (Associative, Commutative, Distributive Laws)

De Morgan’s Laws

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2. Relations

Definition of a Relation (Cartesian Product of Two Sets)

Types of Relations

Empty Relation

Universal Relation

Reflexive Relation

Symmetric Relation

Transitive Relation

Equivalence Relation (A relation that is Reflexive, Symmetric, and Transitive)

Representation of Relations Using Ordered Pairs and Graphs

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3. Function

Definition of a Function (Mapping Between Two Sets)

Types of Functions

One-One (Injective) Function

Onto (Surjective) Function

One-One and Onto (Bijective) Function

Constant Function

Identity Function

Polynomial Function

Rational Function

Modulus Function (|x|)

Greatest Integer Function [x] (Step Function)

Signum Function

Exponential and Logarithmic Functions

Composition of Functions

Inverse of a Function

Graphical Representation of Functions

Even and Odd Functions

Periodic Functions