# Tag Archives: Discrete Mathematics

## Smallest number greater than or equal to N having sum of digits not exceeding S

Given integer N and integer S, the task is to find the smallest number greater than or equal to N such that the sum of… Read More »

## Proof of De-Morgan’s laws in boolean algebra

Statements : 1. 2. Proof: Here we can see that we need to prove that the two propositions are complement to each other. We know… Read More »

## Graph measurements: length, distance, diameter, eccentricity, radius, center

Prerequisite – Graph Theory Basics – Set 1, Set 2 A graph is defined as set of points known as ‘Vertices’ and line joining these… Read More »

## Discrete Mathematics | Hasse Diagrams

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… Read More »

## Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph

Prerequisite – Graph Theory Basics – Set 1 1. Walk – A walk is a sequence of vertices and edges of a graph i.e. if… Read More »

## Inverse functions and composition of functions

Inverse Functions – In mathematics a function, a, is said to be an inverse of another, b, if given the output of b a returns… Read More »

## Mathematics | Introduction to Proofs

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… Read More »

## Mathematics | Independent Sets, Covering and Matching

1. Independent Sets – A set of vertices I is called independent set if no two vertices in set I are adjacent to each other… Read More »

## Mathematics | Sequence, Series and Summations

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… Read More »

## Discrete Mathematics | Representing Relations

Prerequisite – Introduction and types of Relations Relations are represented using ordered pairs, matrix and digraphs: Ordered Pairs – In this set of ordered pairs… Read More »

## Discrete Mathematics | Types of Recurrence Relations – Set 2

Prerequisite – Solving Recurrences, Different types of recurrence relations and their solutions, Practice Set for Recurrence Relations The sequence which is defined by indicating a… Read More »

## Inclusion-Exclusion and its various Applications

In the field of Combinatorics, it is a counting method used to compute the cardinality of the union set. According to basic Inclusion-Exclusion principle: For… Read More »

## Mathematics | Some theorems on Nested Quantifiers

Prerequisite – Predicates and Quantifiers – Set 1, Set 2 Quantifiers are expressions that indicate the scope of the term to which they are attached,… Read More »

## Number of possible Equivalence Relations on a finite set

An equivalence relation is Reflexive, Symmetric and Transitive. Before counting the number of possible equivalence relations on a set |A|=n, let us see an example… Read More »

## Consensus Theorem in Digital Logic

Prerequisite – Properties of Boolean algebra, Minimization of Boolean Functions Redundancy theorem is used as a Boolean algebra trick in Digital Electronics. It is also… Read More »