Basic definition for different types of Sets

Basic topic of mathematics is Sets. Definition of sets were given to you in my previous post. I am here today to give you the basic definition for different types of sets. Lets learn that now.

Different types of Sets and their definition:-

Finite and Infinite Sets: A set is called finite if it contains a specific number of elements. if not, a set is an infinite set.

Null Set or Empty Set or Void Set: A set with no elements is an empty set.

Singleton Set or Singlets: A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is 1.

Equivalent Sets: Two finite sets A and B are said to be equivalent sets if the element of both sets are equal i.e. n (A) = n (B).

Equal Sets: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B.

Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denoted by n(A).

Universal Set: In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set.

Subsets: If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A Í B.

Power Set: The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S).

Now that you know what is a Set now lets learn more on Subset.

Subset:- When set is defined and pieces of the set is taken a subset is formed. Let A and B be two sets. If every element of A contains an element of B, then A is called a subset of B for more details just look at the picture below.

You want to know more just check my next post as i am going to write more details on it.