# Sets

## What is Set?

A set is a collection of well defined objects which are distinct from each other. It means that we can definitely decide whether a given particular object belongs to a given collection or not. The objects, elements and members of a set are synonymous terms.

Set are generally denoted by capital letters A, B, C, D, ……. etc. The elements of set by a, b, c, d, …… etc.

If a is an element of a set A, then we write a ∈ A and say *a* belongs to A.

If *a *does not belong to A then we write *a ∉ A*

## Some Important Numbers Sets:

N = Set of all natural numbers

= {1, 2, 3, 4, …….}

W = Set of all whole numbers

= {0, 1, 2, 3, 4, …….}

Z or I set of all integers

= {….. -3, -2, -1, 0, 1, 2, 3, …..}

Z^{+} = Set of all +ve integers

= {1, 2, 3, ….} = N.

Z^{–} =Set of all -ve integers

= {-1, -2, -3, -4, …….}

Z_{0}= The set of all non-zero integers

={±1, ±2, ±3,…..}

Q = The set of all rational numbers.

= {p/q:p, q∈ I, q ≠ 0}

R = the set of all real numbers.

R-Q =The set of all irrational numbers.

## Set Operations

There are a number of standard (common) operations which are used to manipulate sets,

producing new sets from combinations of existing sets (sometimes with entirely different

types of elements). These standard operations are:

- union
- intersection
- set difference
- symmetric set difference
- complement
- cartesian product