Set

A set is a well-defined collection of distinct objects. The objects that make up a set (also known as the set’s elements or members) can be anything: numbers, people, letters of the alphabet, other sets, and so on.[wikipedia]

For Example:

1. A collection of students going on a trip is a set
2. A collection of whole or integer numbers is a set

Mostly the study of discrete mathematics include discrete structures.

Most important discrete structures are built using sets, that are collection of objects.

We will study the fundamental discrete structures on which all other discrete structures are built, namely set.

Representation of sets:

1. The objects are called the elements or members of the set.
2. Sets are denoted by capital letters A, B, C …, X, Y, Z.
3. The elements of a set are represented by lowercase letters
a, b, c, … , x, y, z.

TABULAR FORM:

Listing all the elements of a set, separated by commas and                         enclosed within braces or curly brackets{} is tabular form

For Example:

In the following examples we write the sets in Tabular Form.

X = {1, 2, 3, 4, 5,6,7,8,9,10}    is the set of first ten Natural Numbers.

Y = {2, 4, 6, 8, …20} is the set of Even numbers up to 20.

Z = {1, 3, 5, 7, 9, …} is the set of positive odd numbers.

Descriptive Form:

Stating in words the elements of a set is descriptive form

For Example:

A=Set of Prime Numbers (is the descriptive form)

B=Set of even numbers up to 50( is the descriptive form)

Set Builder Form:

Writing the elements of set in symbolic form is Set builder form

For Example:

A = {x ∈ E / 0 < x <=50}

B = {x ∈ N / x<=5}

SUBSET:

If every member of set A is also a member of set B, then A is said to be a subset of B, written A ⊆ B (also pronounced A is contained in B). Equivalently, we can write B ⊇ A, read as B is a superset of AB includes A, or B contains A. [wikipedia]

[