Page no:25
MT11-Discrete Mathematics Objective : This is the first mathematics subject which revises the knowledge
acquired previously by the student. Logic, Relations and Functions, Algebraic Functions and Graph Theory will be introduced in this course. Sr. No 1 Nos. of Session Reference Books
Chapter Details Mathematical logic Propositions (Statements) Logical connectivity’s, N, A ,V, ?,?, ? Compound statements form, truth tables, tautology, implications and equivalence of statements forms logical identities Normal forms: disjunctive normal form and simplification. Conjunctive normal form, logical implications, valid arguments, methods of proof. Theory of inference of statement calculus, predicate calculus, qualifiers free and bound variables, theory of inference of predicate calculus. Relations and functions: Relation defined as ordered n-tuple Unary, binary, ternary, n-ary Restrict to binary relations Complement of a relation, converse Relation , compositions, matrix representation and its properties Graphical representation of relation – Digraphs Properties of binary relation – Reflexive, irreflexive, symmetric, Asymmetric, transitive Equivalence, equivalence classes, partitions covering, compatible relation maximal compatibility block, transitive closure – Warshall’s algorithm. Partial ordering relation – Hesse diagram, Chains and antichains. Lattice , maximal and minimal elements, upper bound , lower bound , definitions Functions – definitions: Partial function, hashing functions, characteristic functions, floor functions, ceiling
2 2 2 2 2 1 1 1 1 1 2 1 1 1 1,2,3,4
2
1 1