LECTURE NOTES BY DR.B.RAMA DEVI

                                                            Propositional Logic: Pro positional calculus   is a branch of  logic . It is also called  propositional logic ,  statement logic ,  sentential calculus ,  and sentential logic. There is a need to develop a formal language to state the Rules and Theory. - A formal language is one in which the syntax is well defined. - This formal language is called an object language.  An object language consists of declarative sentences. These can have two truth values 'T' or 'F', denoting whether the statement is True or False. Declarative Statement : A  statement  is said to be declarative if has a truth value, i.e. T or F. Proposition: A proposition is a declarative statement that is either True or False, but not both.   Atomic Statement : A statement is said to be  atomic  if it cannot be divided into smaller statements. Otherwise, it is called  molecular . Propositional consists of propositional variables

UNIT – I   Mathematical Logic : Propositional Calculus: Statements and Notations, Connectives, Truth Tables, Tautologies, Equivalence of Formulas, Duality law, Tautological Implications, Normal Forms, Theory ofInference for Statement Calculus, Consistency of Premises, Indirect Method of Proof. Predicate calculus : Predicative Logic, Statement Functions, Variables and Quantifiers, Free & Bound Variables, Inference theory for predicate calculus. UNIT – II Set Theory : Introduction, Operations on Binary Sets. Relations: Properties of Binary Relations, Relation Matrix and Digraph, Operations on Relations, Partition and Covering, Transitive Closure, Equivalence, Compatibility and Partial Ordering Relations, Hasse Diagrams. Functions:Bijective Functions, Composition of Functions, Inverse Functions, Permutation Functions,Recursive Functions.  UNIT - III Graph Theory I: Basic Concepts of Graphs, Sub graphs, Matrix Representation of Graphs: AdjacencyMatrices, Incidence Matrices, Is

LAKIREDDY BALI REDDY COLLEGE OF ENGINEERING (AUTONOMOUS), MYLAVARAM B.Tech. (IV Sem.) 17CI03 - DISCRETE MATHEMATICAL STRUCTURES   Pre-requisites: Basic Mathematical Knowledge Course Educational Objective: Perform the operations associated with sets, functions, and relations. Relate practical examples to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context. Use formal logic proofs and/or informal but rigorous logical reasoning to, for example, predict the behavior of software or to solve problems such as puzzles. Course Outcomes : At the end of the course, the student will be able to:  CO1:  Illustrate basic concepts of mathematical logic and predicate                                               CO2:  Analyze the Sets, Relations and Functions concepts .  CO3:  : Importance of Graph theory and its real time applications CO4:  Elaborate Algebraic Structures, Pigeonhole Principle and its Real time applicati