set theory

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 = ..

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 ..

Example: - In a class of 80 boys, there are 60 boys who play rugby and 35 play tennis. Use Venn diagrams to show how many boys play both the games? How many play rugby only and how many play tennis onl..

A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set..

This method is also known as Property method. In this method, a set is represented by stating all the properties which are satisfied by the elements of the set and not by any other element. If A contains all values of 'x' for which the condition P(x) is true, then we write A = ..

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..

The total number of all possible subsets of a given set containing n elements is 2 ..

In Mathematics, a well-defined collection of definite objects is called a set. George Cantor is regarded as the "Father of Set theory". The concept of "Sets" is basic in all branches of mathematic..

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 the other set. T..