# kinds of sets

There are different types of sets.

Empty Set

A set does not have an element called an empty set. It is denoted by {} or ϕ.

Example 1:

X={x: x is a vowel between o and u}

As we that there is no vowel between o and u.

Therefore X is empty.

Finite set

A set having a finite number of elements is called a finite set. Finite mean countable.

Example:

X = { x | x ∈ N and 20 > x > 10 }

Infinite Set

A set having an infinite number of elements is called an infinite set. Infinite means are uncountable.

Example

Y= { x | x ∈ W and x > 70 }

Subset:

A set X is a subset of Y if set X is contained in set Y. The set is written as X\subseteq Y . All the elements of set X contain in set Y.

Example

Suppose  A={3,6,9,12,15}      ,    B={3,6}

We can say

B\subseteq A

Because all the elements of set B contain in set A.

Power Set

Suppose X be a set, the set of all the possible subsets of a set x is called the power set of X . It is denoted by P(X). We can find the number of subsets by using [katex]2^n[/katex].

X ={1,2}

By using [katex]2^n[/katex] we find the number of subsets. In this set, the number of subsets is 4.