# Discrete Mathematics

Introduction to discrete mathematics pdf:

Discrete mathematics is part of 3 main topics

Mathematics Logic

Boolean Algebra

Graph Theory

discrete mathematics pdf-Mathematics Logic

The find of logic which is used in mathematics is called deductive logic. Mathematical arguments must be strictly deductive in nature. In other words, the truth of the statements to be proved must be established assuming the truth of some other statements.

For example, in geometry we deduce the statement the statement that he sum of the three angles of a triangle is 180 degrees from the statement that an external angle of a triangle is equal to the sum of the other (i.e., opposite) two angles of the triangles of the triangle.

The kind of logic which we shall use here is bi-valued i.e. every statement will have only two possibilities, either True' or 'False' but not both.

Definition:- The symbols, which are used to represent statements, are called statement letters or sentence variables.

To represent statements usually the letters P, Q, R, ..., p, q, r, ... etc., are used

discrete mathematics pdf-Boolean algebra

Boolean algebra was firstly introduced by British Mathematician George Boole (1813 - 1865).the original purpose of this algebra was to simplify logical statements and solve logic problems. In case of Boolean algebra, there are mainly three operations (i) and (ii) or and (iii) not which are denoted by '^^' ,'vv' and (~) respectively. In this chapter, we will use +, . , ' in place of above operations respectively.

Definition:-Let B be a non-empty set with two binary operations + and ., a unary operation ' and two distinct elements 0 and 1. Then B , +, . ,' is called Boolean algebra, if the following axioms are satisfied.

discrete mathematics pdf-Graph theory

Graphs appear in many areas of mathematics, physical, social, computer sciences and in many other areas. Graph theory can be applied to solve any practical problem in electrical network analysis, in circuit layout, in operations research etc.

By a graph, we always mean a linear graph because there is no such thing as a non-linear graph. Thus in our discussion we shall drop the adjective 'linear', and will say simply a 'graph'

Definition:- A graph G = (V, E) consists of a set of objects V = (v1, v2, ...), whose elements are called vertices (or points or nodes) and an another set E = {e1, e2, ....} whose elements are called edges (or lines or branches) such that each ek is identified with an unordered pair (vi, vj) of vertices. The vertices vi and vj associated with the edge ekare said to be the end vertices of ek.