 # DISCRETE STRUCTURES AND GRAPH THEORY

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SYLLABUS
Unit-I
Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs,Set Identities.
Relations: Definition, Operations on relations, Properties of relations, Composite Relations,
Equality of relations, Order of relations.
Functions: Definition, Classification of functions,Operations on functions, Recursively
defined functions.
Natural Numbers: Introduction, Mathematical Induction, Variants of Induction, Induction
with Nonzero Base cases.
Unit-II
Algebraic Structures: Definition, Groups, Subgroupsand order, Cyclic Groups,
Cosets,Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group
Homomorphisms, Definition and elementary propertiesof Rings and Fields, Integers Modulo n.
Unit-III
Partial order sets: Definition, Partial order sets,Combination of partial order sets, Hasse
diagram.
Lattices: Definition, Properties of lattices – Bounded, Complemented, Modular and Complete
Lattice,Morphisms of lattices.
Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic
manipulation of Boolean expressions. Simplificationof Boolean Functions, Karnaugh maps,
Logic gates, Digital circuits and Boolean algebra. Combinational and sequential Circuits.
Unit-IV
Propositional Logic: Proposition, well formed formula, Truth tables, Tautology, Satisfiability,
Contradiction, Algebra of proposition, Theory of Inference ,Natural Deduction.
Predicate Logic: First order predicate, well formedformula of predicate, quantifiers, Inference
theory of predicate logic.
Unit-V
Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.
Graphs: Definition and terminology, Representation of graphs, Multigraphs, Bipartite graphs,
Planar graphs, Isomorphism and

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