SEMESTER V MA1301 – DISCRETE MATHEMATICS

 ANNA UNIVERSITY TIRUCHIRAPPALLI
Tiruchirappalli - 620 024 
SEMESTER V MA1301  –  DISCRETE MATHEMATICS

 
UNIT I   PROPOSITIONAL CALCULUS                                      9
Propositions   − Logical Connectives   − Compound Propositions   − Conditional and Biconditional
Propositions   − Truth Tables   − Tautologies and Contradictions   − Contrapositive   − Logical
Equivalences and Implications  − Demorgan’s Laws  − Normal Forms  − Principal Conjunctive and
Disjunctive Normal Forms − Rules of Inference − Arguments − Validity of Arguments.

UNIT II  PREDICATE CALCULUS                                            9 
Predicates − Statement Function − Variables − Free and Bound Variables − Quantifiers − Universe of
Discourse − Logical Equivalences and Implications for Quantified Statements − Theory of Inference −
The Rules of Universal Specification and Generalization −Validity of Arguments.

UNIT III  SET THEORY                                         9 
Basic Concepts − Notations − Subset − Algebra of Sets − The Power Set − Ordered Pairs and Cartesian
Product  − Relations on Sets  − Types of Relations and their Properties  − Relational Matrix and the
Graph of a Relation − Partitions − Equivalence Relations − Partial Ordering − Poset − Hasse Diagram
− Lattices and their Properties − Sublattices − Boolean Algebra − Homomorphism.

UNIT IV  FUNCTIONS                                         9 
Definition of functions − Classification of Functions − Type of Functions − Examples − Composition
of Functions − Inverse functions − Binary and n-ary Operations − Characteristic Function of a Set −
Hashing Functions − Recursive Functions − Permutation Functions.

UNIT V  GROUPS                                         9 
Algebraic Systems − Definitions − Examples − Properties − Semigroups − Monoids − Homomorphism
− Sub Semigroups and Submonoids − Cosets and Lagrange’s Theorem − Normal Subgroups −Normal
Algebraic System with two Binary Operations − Codes and Group Codes − Basic Notions of Error
Correction − Error Recovery in Group Codes.
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                       L: 45 T: 15 Total: 60   

TEXT BOOKS
1.  Trembly J.P and Manohar R, “Discrete Mathematical Structures with Applications to Computer
Science”, TMH Pub. Co. Ltd, New Delhi, 2003.
2.  Ralph P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied Introduction”,
Fourth Edition, Pearson Education Asia, Delhi, 2002.

REFERENCES
1.  Bernard Kolman, Robert C. Busby and Sharan Cutler Ross, “Discrete Mathematical
Structures”, Fourth Indian reprint, Pearson Education Pvt Ltd., New Delhi, 2003.
2.  Kenneth H. Rosen, “Discrete Mathematics and its Applications”, Fifth Edition, TMH Pub. Co.
Ltd., New Delhi, 2003.
3.  Richard Johnsonbaugh, “Discrete Mathematics”, Fifth Edition, Pearson Education Asia, New
Delhi, 2002.
 

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