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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.
    1. 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.
    2. 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.



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