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Discrete Mathematics

This is the collection of Sikkim Manipal University (SMU) question and answers for Discrete Mathematics. It will help to prepare your examination. All question paper are classified as per semester, subject code and question type of Part A, Part B and Part C with multiple choice options as same as actual examination. SMU question papers includes year 2024, 2023, 2022 Sem I, II, III, IV, V, VI examinations of all subjects.

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Course Name        MSc IT (Master of Science in Information Technology)

Subject Code       MT0043 (Discrete Mathematics)

Get Questions        PART - A    PART - B    PART - C

Discrete Mathematics Syllabus.

Unit 1: Mathematical Logic
Proposition or statements, connectives, Tautology, normal forms, well formed formulas, predicate calculus

Unit 2: Set Theory
Sets, operation on sets, principles of inclusion and exclusion, Peano’s axiom and mathematical induction, generating functions, recurrence relations

Unit 3: Relations
Product set and partitions, relations, properties of relations, manipulation of relations

Unit 4: Functions
Types of functions, pigeonhole principle , permutations and combinations, combinatorics-simple counting principle

Unit 5: Order relations and structure
Partially ordered sets, Hasse diagram, external elements of posets, lattices

Unit 6: Semigroups and Coding
Binary operation, semi groups, products and quotients of semi groups , groups , subgroups , cosets, cyclic groups , coding and decoding , error detection and correction

Unit 7: Graphs
Introduction to graphs , digraphs , paths, cycles , degrees , complete graphs , bipartite graphs , connectivity , bridges , blocks , trees , subgraphs , spanning

Unit 8: Traversability
Eulerian graphs, characterization, Hamitonian paths and circuits , traveling salesman problem

Unit 9: Covering and Independence , planarity
Planar graphs, non-planar graphs, Euler’s formula , Colourability

Unit 10: Representation graph
Incidence matrix, Adjacency matrix

Unit 11: Boolean Algebra
Boolean function, duality, Boolean identities, minimal Boolean function, disjunctive normal form, conjunctive normal form , switching circuits

Unit 12: Fuzzy Sets
Introduction, fuzzy set operations, truth value , algebraic operations on fuzzy sets , generation of rules for fuzzy problems, fuzzy propositions , applications of fuzzy sets

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