Discrete Mathematics - IN SEM for SPPU 19 Course (SE - I - Comp.- 210241)  (Paperback, Dr.H.R.Bhapkar, Dr. Rajesh N. Phursule)

Unit I Set Theory and Logic Introduction and significance of Discrete Mathematics, Sets – Naïve Set Theory (Cantorian Set Theory), Axiomatic Set Theory, Set Operations, Cardinality of set, Principle of inclusion and exclusion, Types of Sets - Bounded and Unbounded Sets, Diagonalization Argument, Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets, Power set, Propositional Logic - logic, Propositional Equivalences, Application of Propositional Logic - Translating English Sentences, Proof by Mathematical Induction and Strong Mathematical Induction. (Chapters - 1, 2, 3) Unit II Relations and Functions Relations and their Properties, n-ary relations and their applications, Representing relations, Closures of relations, Equivalence relations, Partial orderings, Partitions, Hasse diagram, Lattices, Chains and Anti-Chains, Transitive closure and Warshall‘s algorithm. Functions - Surjective, Injective and Bijective functions, Identity function, Partial function, Invertible function, Constant function, Inverse functions and Compositions of functions, The Pigeonhole Principle. (Chapters - 4, 5)