Set Theory

Sets: Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a set of real numbers especially intervals (with notations). Universal set. Power set. Set operations(Union and Intersection of sets, Difference of sets, Complement of a set) with algebraic properties,  Venn diagrams.

Relations: Ordered pairs. Cartesian product of sets. Definition of relation, pictorial diagrams, domain, co-domain and range of a relation.

Types of relations: reflexive,  symmetric, Anti-symmetric, transitive and equivalence relations with examples.

Functions: Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions: domain and range of these functions, composite functions,Invertible functions.

Type of functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.One to one and onto functions.