SETSA set is a well-defined and unordered collection of objects, called elements or members of

the set.

In the above definition of sets well-defined means, it is possible to decide if a given object belongs to the set or not.

Unordered means that the order in which the objects of set are listed is not important.

Example: A = {2, 3, 5, 7} is a set of prime numbers less than 10.

In the above example, “2 belongs to/is an element of set A” and is represented by ‘’2 ∈ A”. “13 does not belong to/is not an element of set A” and is represented by “13 ∉ A”.

NOTE: In general, we use upper case letters to denote sets and lower case letters to denote members or elements of the set.

Specifying a Set

There are two ways to specify a set.

Roster method Set-Builder method

In Roster method, we list all the members of the set between braces.

Example: V = {a, e, i, o, u} is a set of vowels.

In Set-Builder method, we list the condition that an object must satisfy to become member of the set.

Example: V = {x | x is a vowel}.

NOTE:

N = {0, 1, 2, 3, . . .}, the set of natural numbers.Z = {. . . ,−2,−1, 0, 1, 2, . . .}, the set of integers.Z+ = {1, 2, 3, . . .}, the set of positive integers.Q = {p/q | p ∈ Z, q ∈ Z, and q ≠ 0}, the set of rational numbers.Q+ = the set of positive rational numbers.Q* = the set of non-zero rational numbers.R = the set of real numbers.R+ = the set of positive real numbers.R* = the set of non-zero real numbers.C = {x + iy | x, y ∈ R, i2 = -1}, the set of complex numbers.C* = the set of non-zero complex numbers.

Type of Sets

Null Set : A set with no elements. It also referred to as an Empty set, denoted by { } or φ.

Singleton Set: A set with only a single element.

Finite Set: A set which has n distinct elements, where n is a positive integer.

Infinite Set: A set in which number of elements cannot be defined.