Prerequisite: Predicates and Quantifiers Set 2, Propositional Equivalences Every Theorem in Mathematics, or any subject for that matter, is supported by underly
Union Union of the sets A and B, denoted by A ∪ B, is the set of distinct element belongs to set A or set B, or both. Above is the Venn Diagram of A U B. Exam
Algebraic Structure A non empty set S is called an algebraic structure w.r.t binary operation (*) if it follows following axioms: Closure:(a*b) belongs to S for
Relations can be used to order some or all the elements of a set. For instance, the set of Natural numbers is ordered by the relation such that for every ordere
Prerequisite – Introduction and types of Relations Relations are represented using ordered pairs, matrix and digraphs: Ordered Pairs – In this set of ordere
Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects
Mathematical proof is an argument we give logically to validate a mathematical statement. In order to validate a statement, we consider two things: A statement
Prerequisite – Generating Functions-Introduction and Prerequisites In Set 1 we came to know basics about Generating Functions. Now we will discuss more detail
SEQUENCE: It is a set of numbers in a definite order according to some definite rule (or rules). Each number of the set is called a term of the sequence and its
Prerequisite – Combinatorics Basics Several Counting problems require finding the number of ways to arrange a certain number of distinct elements, where the r
Prerequisite – Generalized PnC Set 1 Combinatorial problems can be rephrased in several different ways, the most common of which is in terms of distributing b
A Hasse diagram is a graphical representation of the relation of elements of a partially ordered set (poset) with an implied upward orientation. A point is draw
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 pi
Conditional probability P(A | B) indicates the probability of event ‘A’ happening given that event B happened. We can easily understand the above formula us
Probability refers to the extent of occurrence of events. When an event occurs like throwing a ball, picking a card from deck, etc ., then the must be some prob
Prerequisite – PnC and Binomial Coefficients So far every problem discussed in previous articles has had sets of distinct elements, but sometimes problems may
Prerequisite – Graph Theory Basics Given an undirected graph, a matching is a set of edges, such that no two edges share the same vertex. In other words, matc
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 brac
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 particul
Antiderivative – Defination :A function ∅(x) is called the antiderivative (or an integral) of a function f(x) of ∅(x)’ = f(x). Example : x4/4 is an anti
Covariance and Correlation are two mathematical concepts which are commonly used in the field of probability and statistics. Both concepts describe the relation
Hypergeometric Distribution Model is used for estimating the number of faults initially resident in a program at the beginning of the test or debugging process
Introduction Two logical expressions are said to be equivalent if they have the same truth value in all cases. Sometimes this fact helps in proving a mathematic
Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. H
