Set Theory Introduction

In this class, We discuss Set Theory Introduction.

The reader can take a complete discrete mathematics course. Click Here.

Set: A collection of well-defined objects is called a set.

Examples:

The Set of vowels of the alphabet.

A Set consists of all positive integers.

The Set Consists of people living on this planet.

Objects in the Set are called members or elements.

The Set is represented using upper case.

Lowercase is used to represent elements in a set.

SET is defined in two ways.

1) Tabular Form

A = {1, 2, 3, 4, 5, 6}

2) Set builder form

A = { x/x is an even integer}

Some Standard Symbols:

N: Set of all natural numbers

Z: Set of all integers

Z+: Set of all positive integers

Z*: The Set of all non-zero integers

E: The Set of all even integers

Q: The Set of all rational numbers

Q*: The Set of all non-zero rational numbers

Q+: The Set of all positive rational numbers

R: The Set of all real numbers

R*: The Set of all non-zero rational numbers

R+: The Set of all positive real numbers

C: The Set of all complex numbers

C*: The Set of all non-zero complex numbers