RCA103 Discrete Mathematics UNIT-1 Set Theory: Introduction, Size of sets and cardinals Venn diagrams, Combination of sets, Multisets, Ordered pairs and Set identities. Relations & Functions: Relations - Definition, Operations on relations Composite relations, Properties of relations quality of relations, Partial order relation Functions - Definition, Classification of functions Operations on functions, Recursively defined functions Notion of Proof: Introduction, Mathematical Induction Strong Induction and Induction with Nonzero base cases UNIT-2 Lattices: Introduction, Partial order sets Combination of partial order sets, Hasse diagram Introduction of lattices, Properties of lattices Bounded, Complemented, Modular and Complete lattice UNIT-3 Boolean Algebra: Introduction, Axioms Theorems of Boolean algebra, Boolean functions Simplification of Boolean Functions, Karnaugh maps Logic gates, Digital circuits and Boolean algebra UNIT-4 Logic gates, Digital circuits and Boolean algebra Tautology, Contradiction, Algebra of propositions Theory of Inference and Natural Deduction Theory of predicates, First order predicate Predicate formulas, quantifiers, Inference theory of predicate logic UNIT-5 Recurrence Relations: Introduction, Growth of functions Recurrences from algorithms, Methods of solving recurrences Combinatorics: Introduction, Counting Techniques Pigeonhole Principle, Pólya’s Counting Theory
