Mathematics

The operations which we can perform on the set are set intersection , set union , a  difference of two sets and complement, and the properties related to the operation  on the set . The operations on set are explained as below: Union The union of two sets A and B is a set that consist of all the elements that either belongs to set A or set B or to both. The union is denoted by '⋃' this symbol.   For example : suppose that, group A consists of five group members named, Smita, Sakshi, Monali, Akash, and Kiran, and group B consist of four members, named as  Akash, Kiran, Sanika, pakhi. The union of these two groups consists of seven members rather than 9, namely Smita, Sakshi, Monali, Akash, Kiran, Sanika, pakhi. A={1,2,3} B={3,4,5,6} A⋃B ={1,2,3,4,5,6} B⋃A ={1,2,3,4,5,6} some properties of operation of union:  A∪B = B∪A                       ( Commutative law ) A∪(B∪C) = (A∪B)∪C     ...

 The types of sets are empty set, singleton set, equivalent sets, equal sets, finite set , infinite set, subsets, super set , proper set, universal set, complement se t .     Empty set or Null set   A  set which doesnot contain any set  is called as Empty set or Null set or Void set. It is denoted by ‘ ∅’ and it is read as phi. In roster form empty set is denoted by {}. The cardinality of null set is always 0. For example: The set set of whole number less than 0. The set of even prime number less than 2.   Singleton set a set which contain only one element is called as singleton set. The cardinality of singleton set is always 1. For example: The set of even prime numbers. A = {2}, | A | = 1 A = {x|x is a whole number less than 1} S = {x|X is a natural number, x*x=4}   Finite set  A set which has a definite number of elements is called as finite set. The cardinality of finite set is always definite. For example: The...

The set in mathematics is the group of objects and the objects should be distinct. Repetition of objects is not allowed in sets.    The sets are used to define the concepts of relations and functions. the theory of sets is developed by German mathematician Georg Cantor (1845-1918). Definition of Set A set is any collection of distinct in simple way set is a collection of objects specified in such a way that we can determine whether a given object is present in the set or not.  for example : 1. A set of vegetables      2. A set of numbers 3. Set of flowers  4. A set of keys    Elements of a set  The different objects or members present in the set are called as elements of set. The elements of a set are written in any order . the elements present in the set should not be repeated. the elements are denoted by small letters.  Notation  A set is usually denoted by capital letters and the elements of the set are denoted by sma...