Properties of Sets

Properties of Logic

Mathematical Logic

Connectives in Mathematical Logic

The Real Number System

Set Theory

Relations and Functions

Set Overview

SET •A well defined collection of distinct objects is called Set.•The members are called the elements of Set. The elements of the set are generally denoted by the small letters a,b,c,…..x,y,z.•The Sets are generally denoted by the Capital letters A,B,C,…..X,Y,Z.•If x is an element of A, then we say x belongs to A and we write...

Logic - An overview

Logic       Logic is the process by which we arrive at a conclusion from the given statement with a valid reason.Statement       An assertion expressed in words or symbols, which is either true or false but not both at the same time, is known as statement.Truth Value and Truth Table       A truth or falsity of a statement...

Real Numbers - Overview

Real Numbers        A Real Number is any positive or negative number which includes integers, rational and irrational numbers. In simple terms, all the numbers except complex number(numbers which have negative roots/numbers in the form "a + ib") can be called as Real Numbers.Integers        The set of all negative and posi...

Truth Table

Hello Readers!!Please go through this note before reading this!!Truth Table for Logical Connectives(where ' p ' and ' q ' are two statements)1. Negationpq~p~qTTFFTFFTFTTFFFTT2.Conjunctionpqp ᴧ qTTTTFFFTFFFF3.Disjunctionpqp v qTTTTFTFTTFFF4.Conditionalpqp ⇒ qTTTTFFFTTFFT5. Biconditional pqp ⇔ qTTTTFFFTTFFTTautology      ...

Real Numbers- Axioms

Hello Readers!!Click Here for a quick overview of Real numbers before proceeding with this note!!! :) Field Axioms1.Addition axiomi. Closure Property :The sum of real number is always real value.i.e., If {a, b} ϵ R then a+b ϵ Rii. Commutative Property:The sum of two real numbers is the same whatever order they are added.i.e....

Real Numbers - Number Line

Hello Viewers!!Before understanding the number line, please visit this note for the basics. Inequality    An inequality is a relation which shows the comparison between two non-equal numbers or expressions using some mathematical signs.       Mathematical signs used in Inequality:            i.     ≤:    "less than or equal ...

Real Numbers - Absolute Value

Hello Readers!!Go through initial notes of Real Numbers before surfing here!! ^_^Absolute Value    If x is an non- negative real number then its absolute is denoted by |x| which is defined as,                          Properties of Absolute Value1. |x| ≥ x & |x| ≥ -x2. |x| ≥ 0 3. |x|2 = (x)24. 5. |xy| = |x|.|y|6. |...