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### Sets

 Read about sets as taught in schools SETS A well defined collection of objects is called a set. An object belonging to the set is called an element of the set. We normally use capital letters to denote a set and small letters to denote the elements of the set. If 'a' belongs to the set A, it is represented as a ∈ A. If 'a' does not belong to the set A, it is represented as a ∉ A. A set which has no elements is called an empty set, void set or null set. A null set is denoted by the Greek letter Φ. A set with at least one element in it is called a non empty set. We list the elements of a non empty set by property method or listing method. Listing method: Listing method is also known as roster method or tabular method. A set of first five natural numbers is A = {1,2,3,4,5}. This method of representation with listing the elements of the set is called roster method. Property method: This method is also known as set builder method. A method in which the property of the set is described is called the property method. The set A = {1,2,3,4,5} can be represented in the set-builder form as A = {x:x∈W and x<5}. Two sets A and B are said to be equal in every element of  set A is present in the set B and every element of set B is present in set A. A set with only one element is called a singleton set.  A set with finite number of elements is called a finite set. An empty set is considered to be a finite set. SUBSETS A set A is a subset of set B if every element of A is present in B. It is denoted as A⊆B. A set A has an element which is not contained in B. It is denoted as A⊄B A set B has an element which is not contained in A. Every element of A is contained in B then A is called proper subset of B and is denoted as A⊂B The empty set φ is a subset of every set.