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UNIT – I

Formal Logic: Statement, Symbolic Representation and Tautologies, Quantifiers, Predicator and validity, Normal form. Propositional Logic, Predicate Logic, Logic Programming and Proof of correctness.

Proof, Relation and Analysis of Algorithm: Techniques for theorem proving: Direct Proof, Proof by Contra position, Proof by exhausting cares and proof by contradiction, principle of mathematical induction, principle of complete induction. Recursive definitions, solution methods for linear, first-order recurrence relations with constant coefficients, Analysis of Algorithms involving recurrence relations-recursive binary search, quick sort, solution method for a divide-and-conquer recurrence relation.                           

 

UNIT – II

Sets and Combinations: Sets, Subtracts, powersets, binary and unary operations on a set, set operations/set identities, fundamental country principles, principle of inclusion, exclusion and pigeonhole principle, permutation and combination, pascal’s triangles, binominal theorem, representation of discrete structures.

Relation/function and matrices: Rotation, properties of binary rotation, operation on binary rotation, closures, partial ordering, equivalence relation, Function properties of function, composition of function, inverse, binary and n-ary operations, characteristics for, Permutation function, composition of cycles, Boolean matrices, Boolean matrices multiplication.                                                                                                    

 

UNIT – III

Lattices & Boolean Algebra: Lattices: definition, sublattices, direct product, homomorphism Boolean algebra: definition, properties, isomorphic structures (in particulars, structures with binary operations)  subalgebra, direct product and homo-morphism, Boolean function, Boolean expression, representation & minimization of Boolean function.

                                                                                                                      

UNIT – IV

Graph Theory: Terminology, isomorphic  graphs, Euler’s formula (proof) four color problem (without proof) and the chromatic number of a graph, five color theorem. Trees terminology, directed graphs, Computer representation of graphs, Warshall’s, algorithms, Decision Trees,  Euler path & hamiltonian circuits, Shortest path & minimal spanning trees, Depth-first and breadth first searchs, trees associated with DFS & BFS). Connected components, in order, preorder & post order trees traversal algorithms.      

TEXT BOOKS:

1.             Keneth H. Rosen, “Discrete Mathematics and Its Applications”, TMH, 1999.

2.             C.L. Liu, “Elements of Discrete Mathematics”, TMH, 2000.

REFERENCES BOOKS:

1.             Kolman, Busby & Ross, “Discrete Mathematical Structures”, PHI, 1996.

2.             Narsingh Deo, “Graph Theory With Application to Engineering and Computer Science”, PHI, 2004.

3.             J. P. Trembly & P. Manohar, “Discrete Mathematical Structures with Applications to Computer Science”, McGraw Hill, 1997.

4.             Vinay Kumar, “Discrete Mathematics”, BPB Publications, 1998.

 

 

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