Discrete Structures Div H

A man hiked for 10hours and covered a total distance of 45Kms. It is known that he hiked 6Kms in the first hour and only 3Kms in the last hour. Show that he must have hiked at least 9Kms within a certain period of two consecutive hours.

A circumference of a wheel is divided into 36 sector to which the numbers 1,2,3,4,5…36 are assigned in some arbitrary manner. Show that there are three consecutive sectors such that the sum of their numbers is at least 56.

From the integers 1-200, 101 of them are chosen arbitrarily. Show that, among the chosen number there exist two  such that one divides other

SET THEORY: Sets, Combinations of sets, Venn Diagrams, Finite

and Infinite sets, Uncountable infinite sets, Principle of inclusion and

exclusion, Multisets.

SET PPT

COUNTING: The Basics of Counting, Permutations and

Combinations, Binomial Coefficients, Algorithms for generating

Permutations and Combinations, The Pigeonhole Principle.
COUNTING PPT

RELATIONS : Relations and Their Properties, n-ary Relations and Their Applications, Representing Relations , Closures of Relations, Equivalence Relations, Partial Orderings - Chain, Anti chain and Lattice, Groups, Types of Groups.

FUNCTIONS: Surjective, Injective and Bijective functions, Inverse Functions and Compositions of Functions, Recursive Function.

Resource Unit 1 PPT

GRAPH: Graph and Graph Models, Graph Terminology and Types of Graph, Representing Graph and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Single source shortest path- Dijkstra's pseudo code algorithm, Planar Graph. 

Resource Unit 1 PPT

TREES: Introduction, properties of trees, Binary search tree, decision tree, prefix codes and Huffman coding, Spanning Trees and Minimum Spanning Tree - Kruskal‘s and Prim‘s pseudo code algorithms , Case Study- Game Tree.  

Resource Unit 1 PPT