The below given is the Basic sets concepts tutorial which contains the definition and basic concepts of sets. All the basic concepts are explained in a understanding manner with the help of examples. Make use of this set operations tutorial to get an idea on sets.

Basic Sets Concepts Tutorial

Sets

   A set is a collection of well-defined objects. This means that the objects of a set are all distinct, i.e., no two objects are the same.    Generally, sets are named with the capital letters A, B, C, etc. The elements of a set are denoted by the small letters a, b, c, etc. Reading notation If x is an element of the set A, we write x ∈ A. If x is not an element of the set A, we write x ∉ A. Example: Consider the set A = { 4, 8, 5, 9 } If 4 is an element of A, it should be written as 4 ∈ A. If 7 is not an element of A, it should be written as 7 ∉ A. Representation of a set    A set can be represented in any one of the following three ways or forms. (i) Descriptive form (ii) Set-builder form or Rule form (iii) Roster form or Tabular form Descriptive Form    One way to specify a set is to give a verbal description of its elements. It is called as the descriptive form of specification. Example: (i) The set of all natural numbers. (ii) The set of all prime numbers less than 100. (iii) The set of all letters in English alphabets. Set-Builder Form or Rule Form    Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy. Example A = { x : x is a letter in the English alphabet } Roster Form or Tabular Form    Listing the elements of a set inside a pair of braces { } is called the roster form. Example Let Q be the set of even natural numbers less than 15. In roster form we write Q = { 2, 4, 6, 8, 10,12,14 } Note: (i) In roster form each element of the set must be listed exactly once. By convention, the elements in a set should not be repeated. (ii) Let A be the set of letters in the word “coffee”, That is, A = { t, r, u, e }. So, in roster form of the set A the following are invalid. { t, r, e } -------> (not all elements are listed) { t, r, u, u, e } -------> (element ‘f’ is listed twice) (iii) In a roster form the elements in a set can be written in any order. The following are valid roster form of the set containing the elements 2, 3 and 4. { 2, 3, 4 } { 2, 4, 3 } {4, 3, 2 } Each of them represents the same set. (iv) If there are either infinitely many elements or a large finite number of elements, then three consecutive dots called ellipsis are used to indicate that the pattern of the listed elements continues, as in { 5, 6, 7,...... } or { 3, 6, 9, 12, 15,........60 }. (v) Ellipsis can be used only if enough information has been given so that one can figure out the entire pattern.


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