math set theory element

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 = ..

If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

Union of sets - If two sets are given, a set can be formed by using all the elements of the two sets. Such a collection is called the union of the given sets..

Summary - A well-defined collection of definite objects is called a set. In roster method of representing a set, all the elements are listed in the set. In property method of representing a set, all the elements are represented by stating all the pr..

Let U be a universal set, A be any subset of U, then the elements of U which are not in A i.e., U - A is the complement of A w.r.t. U is written as A' = U - A = A c ..

A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is ..

If A and B are two sets, we define their symmetric difference as the set of all elements that belong to A or to B, but not both A and B, and we denote it by A D B. Thu..

In roster method of representing a set, all the elements are listed in the set. Two sets are said to be Equivalent sets if the elements of one set can be put in one-one correspondence with the elements of th..

This method is also known as tabular method. In this method, a set is represented by listing all the elements of the set, the elements being separated by commas and are enclosed within flower brackets {..

Difference of two sets A and B, A - B is a set whose elements belong to A but not to B. A - B is called the relative complement of B w.r.t. ..