Unit 1: Set Theory, Relation, Function, Theorem Proving Techniques

Topics

• Definition of sets →
• countable and uncountable sets →
• Venn Diagrams →
• proofs of some general identities on sets →
• Relation: Definition →
• types of relation →
• composition of relations →
• Pictorial representation of relation →
• Equivalence relation →
• Partial ordering relation →
• Job-Scheduling problem →
• Function: Definition →
• type of functions →
• one to one →
• into and onto function →
• inverse function →
• composition of functions →
• recursively defined functions →
• pigeonhole principle →
• Theorem proving Techniques: Mathematical induction →
• Proof by contradiction →