Double Math

kinds of sets

There are different types of sets.

1. Empty set 7. Infinite set
2. Power set8. Singleton set
3. Superset9. subset
4. Equal set10. Proper set
5. Equivalent set11. Improper set
6. Finite set 12. Universal set

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.


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.


Y= { x | x ∈ W and x > 70 }


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. 


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 2^n.

X ={1,2}

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