## Mathematics | Introduction to Propositional Logic | Set 2

Prerequisite : Introduction to Propositional Logic – Set 1 De Morgan’s Law : In propositional logic and boolean algebra, De Morgan’s laws are a pair… Read More »

## Mathematics | Rules of Inference

Prerequisite: Predicates and Quantifiers Set 2, Propositional Equivalences Every Theorem in Mathematics, or any subject for that matter, is supported by underlying proofs. These proofs… Read More »

## Mathematics | Predicates and Quantifiers | Set 2

Prerequisite : Predicates and Quantifiers Set 1, Propositional Equivalences Logical Equivalences involving Quantifiers Two logical statements involving predicates and quantifiers are considered equivalent if and… Read More »

## Prosecutor’s Fallacy

Prosecutor’s fallacy is a very famous but neglected application of Baye’s rule. Prosecutor’s fallacy is a fallacy in statistical reasoning. This very famous problem uncovers… Read More »

## Mathematics | Algebraic Structure

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… Read More »

## 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… Read More »

## Mathematics | Representations of Matrices and Graphs in Relations

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… Read More »

## Mathematics | Introduction and types of Relations

Relation or Binary relation R from set A to B is a subset of AxB which can be defined as aRb ↔ (a,b) € R… Read More »

## Mathematics | System of Linear Equations

Trace of a matrix : Let A=[aij] nxn is a square matrix of order n, then the sum of diagonal elements is called the… Read More »

## Mathematics | Random Variables

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… Read More »

## Mathematics | Classes (Injective, surjective, Bijective) of Functions

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… Read More »

## 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,… Read More »

## Mathematics | Lagrange’s Mean Value Theorem

Suppose be a function satisfying three conditions: 1) f(x) is continuous in the closed interval a ≤ x ≤ b 2) f(x) is differentiable in… Read More »

## Mathematics | Rolle’s Mean Value Theorem

Suppose f(x) be a function satisfying three conditions: 1) f(x) is continuous in the closed interval a ≤ x ≤ b 2) f(x) is differentiable… Read More »

## Mathematics | Eigen Values and Eigen Vectors

Eigen vector of a matrix A is a vector represented by a matrix X such that when X is multiplied with matrix A, then the… Read More »