Types of sets

In this tutorial I will discuss the different types of sets.

Finite set:

A set which contains finite number of elements is known as finite set. Consider the following examples:

A={a,b,c,d}

B={1,5,8,34,78}

Infinite set:

A set which contains infinite number of elements is known as infinite set. Consider the following examples:

N={1,2,3,4,………}

I={…….,-3,-2,-1,0,1,2,3,……..}

Singleton set:

A set which contains only one element is known as singleton set. Consider the following set:

A={7}

B={q}

Pair set:

A set which contains only two elements is known as a pair set. Consider the examples:

S={1,5}

S={{1,2},{a,b,d}}

Empty Set:

A set which contains no element is known as empty set. The empty set is also known as void set or null set. Generally denoted by phi( Φ) . Consider the examples:

Φ={x | x≠x}

Φ={x | x is a month of the year containing 56 days}

Set of Sets:

A set which contains sets is known as set of sets. Consider the example:

S={{3,5,7,8},{a,f,h,t,i},{apple,mango,orange},{5}}

Universal Set:

A set which is super set of all the set under consideration or particular discussion is known as universal set. Generally denoted by U or E or Ω. consider the example:

Let

  A={a,b,c}

B={a,e,i,o,u}

C={p,q,r,t}

So, we can take the universal set as follows.

U={a,b,c,d,e…….,z}