# Category Archives: Mathematics

## Matrix Introduction

A matrix represents a collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets. A matrix with 9 elements is shown below. This Matrix [M] has 3 rows and 3 columns. Each element of matrix [M] can be referred to… Read More »

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## Relations |Representations in Matrices and Graphs

Previously, we have already discussed Relations and their basic types. Combining Relation: Suppose R is a relation from set A to B and S is a relation from set B to C, the combination of both the relations is the relation which consists of ordered pairs (a,c) where a Є A and c Є C… Read More »

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## Relations in Discrete Mathematics | Introduction and their types

Relation or Binary relation R from set A to B is a subset of AxB which can be defined as aRb <=> (a,b) € R <=> R(a,b). A Binary relation R on a single set A is defined as a subset of AxA. For two distinct set, A and B with cardinalities m and n,… Read More »

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## Random Variable

Random variable is basically a function which maps from the set of sample space to set of real numbers. The purpose is to get an idea about result of a particular situation where we are given probabilities of different outcomes. See below example for more clarity. Example : Suppose that two coins (unbiased) are tossed… Read More »

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## Functions | Properties and Types (Injective, surjective, Bijective)

A function f from A to B is an assignment of exactly one element of B to each element of A (A and B are non-empty sets). A is called Domain of f and B is called co-domain of f. If b is the unique element of B assigned by the function f to the… Read More »

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## Discrete Mathematics | The Pigeonhole Principle

Suppose that a flock of 20 pigeons flies into a set of 19 pigeonholes to roost. Because there are 20 pigeons but only 19 pigeonholes, a least one of these 19 pigeonholes must have at least two pigeons in it. To see why this is true, note that if each pigeonhole had at most one… Read More »

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