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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 2022, 2021, 2020 Sem I, II, III, IV, V, VI examinations of all subjects.

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Course Name        MCA (Master of Computer Application)

Subject Code       MC0063 (Discrete Mathematics)

Get Questions        PART - A    PART - B    PART - C

Discrete Mathematics Syllabus.

Part 1: Sets, Relations and Functions
Sets; Relations; Functions; Intervals; Functions of real variables; Different functions.

Part 2: Mathematical Induction
Progressions; Principle of Mathematical Induction; Summation of series using n, n2 and n3.; Arithmetico – Geometric series (A.G.P); Summation of series by the Method of Differences and partial fractions.

Part 3: Combinatorics
Principles of Counting; Generating Function; Partitions and Compositions; Orderings; Principle of Inclusion and Exclusion.

Part 4: Recurrences and Integer
Functions Recurrence Relation; Applications of Recurrences; Generating Function; Integer Functions.

Part 5: Partially Ordered Sets and Lattices
Relation Matrices; Partial Ordered Sets; Lattices; Duality; Modular and Distributive lattices.

Part 6: Semigroups, Monoids and Groups
Semigroups; Monoids; Groups; Permutation Groups.

Part 7: Rings, Fields and Vector Spaces
Rings and Integral domains; Fields; Vector Spaces.

Part 8: Propositional Calculus and Logical Quantifiers
Logical Inference; Propositions and Tautologies; Predicates; Logical Quantification of Propositions.

Part 9: Preliminaries
Sets; Functions; Equivalence Relations; Algebraic Systems; Algorithms.

Part 10: Theory of Numbers and Introduction to Cryptography
Divisibility and Factorization; Congruence; Arithmetical Functions; Method of Repeated Squares; Applications to Cryptography.

Part 11: Formal Languages
Grammars and Languages; Classification of Grammars; Backus – Naur Form (BNF); Derivation Trees.

Part 12: Boolean Algebras and Logical Circuits
Posets and Lattices; Boolean lattices and Boolean algebras; Uniqueness of finite Boolean algebras; Boolean Expressions and Normal forms; Logical circuits and applications.

Part 13: Finite – State Automata
Finite State Machine; Non – Determinants Finite State Automaton (NDFSA); Languages accepted by an automation; Turing Machine.

Part 14: Algebraic Codes
Preliminaries; Hamming Distance; Linear Codes; Parity Check, Generator Matrices.

Part 15: Fuzzy Sets and Fuzzy Logic
Fuzzy sets; Fuzzy Relations; Classical logic and Fuzzy logic; Linguistic variable; Fuzzy Truth Qualifier.

Part 16: Graphs
Preliminary Definitions and Notations.

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