![]() UNIT - III: Group Theory (12 Hrs) Binary Operations, Properties, Semigroups, Monoids,Subsemigroup,Submonoid, Isomorphism & Homomorphism,, Groups (only definitions and examples) Subgroups and Homomorphism, Cosets and Lagrange’s Theorem, Normal subgroups. ![]() Functions: Definition, Composition of functions, Types of Functions, Invertible Function, Permutation Function, Characteristics function of a set with Theorems. UNIT - II: Relations and Functions (12 Hrs) Relations: Ordered pairs and n-tuples, Product Sets and Partitions, Relations and Digraphs, Matrix of Relation, Paths in Relations and Digraphs, Properties of Relations, Equivalence Relations & Partitions, Compatible Relation, Manipulationof Relations, Composition of Relations, Transitive Closure of a relation, Partial order relation, Partially ordered set, Hasse Diagrams. Basic concepts of set theory, Operations on Sets, The power set. College Assessment: 20 Marks University Assessment: 80 Marks Subject Code: BE4S1T UNIT - I: Mathematical Logic and Set Theory (08 Hrs) Propositions and Logical Operations, Quantifiers, Conditional Statements and Tautologies, Methods of Proof, Principle of Mathematical Induction. Fourth Semester (Computer Science & Engineering) DISCRETE MATHEMATICS AND GRAPH THEORY Duration: 3 Hr.
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