Notes On Representation of Sets - CBSE Class 11 Maths
A set is a well-defined collection of objects. By well-defined collection, we mean that we should be able to decide whether a particular object belongs to a definite collection or not. Example of a well-defined collection is natural numbers less than five. This collection of natural numbers is well defined, as we can definitely decide whether a given particular number belongs to this collection or not. An example of a set that is not well defined is a set that consists of clever students. This is a not a well-defined set because the choice of clever students is not clear, since there is no accurate measure for cleverness. A set is denoted with a capital letter. E.g.: A, Q, S The elements of a set are denoted with small letters. e.g.: x, p, s, etc. The word element is used synonymously with the words object and member. A= {p, q, r} The element p belongs to set A. p ∈ A z ∉ A N : The set of natural numbers Z : The set of integers Q : The set of integers R : The set of real numbers Z+ : The set of positive integers Q+ : The set of positive rational numbers R+ : The set of positive real Numbers There are two ways of representing sets. 1. Roster form 2. Set-builder form Roster form This method of representing sets is also called the tabular form. Ex: Prime numbers less than 10. P = {2, 3, 5, 7} Similarly, a set of natural numbers between 20 and 30 is represented as: A = {21, 22, 23, 24, 25, 26, 27, 28, 29} The order of the elements in a set is unimportant. While representing a set in roster form, the elements are generally not repeated. Only distinct elements are written while representing a set in roster form. Set-builder form The set-builder form is a more concise form of a given set. To write the set in the set-builder form, start with a bracket and write the variable. Then a colon is placed and a property is assigned to this number. Ex 1: {2, 3, 5 and 7} is written in set-builder form as P = {x:x is a prime number, x < 10}. The set is named as P and read as P is the set of all x such that x is a prime number less than 10. Ex 2: Represent the set of natural numbers between 20 and 30 using the set-builder form. Set of natural numbers between 20 and 30 = {21, 22, 23, 24, 25, 26, 27, 28, 29} We name this set A. A = {n:n is a natural number, 20 < n < 30} This is read as: A is the set of all n such that n is a natural number and n is lies between 20 and 30.

#### Summary

A set is a well-defined collection of objects. By well-defined collection, we mean that we should be able to decide whether a particular object belongs to a definite collection or not. Example of a well-defined collection is natural numbers less than five. This collection of natural numbers is well defined, as we can definitely decide whether a given particular number belongs to this collection or not. An example of a set that is not well defined is a set that consists of clever students. This is a not a well-defined set because the choice of clever students is not clear, since there is no accurate measure for cleverness. A set is denoted with a capital letter. E.g.: A, Q, S The elements of a set are denoted with small letters. e.g.: x, p, s, etc. The word element is used synonymously with the words object and member. A= {p, q, r} The element p belongs to set A. p ∈ A z ∉ A N : The set of natural numbers Z : The set of integers Q : The set of integers R : The set of real numbers Z+ : The set of positive integers Q+ : The set of positive rational numbers R+ : The set of positive real Numbers There are two ways of representing sets. 1. Roster form 2. Set-builder form Roster form This method of representing sets is also called the tabular form. Ex: Prime numbers less than 10. P = {2, 3, 5, 7} Similarly, a set of natural numbers between 20 and 30 is represented as: A = {21, 22, 23, 24, 25, 26, 27, 28, 29} The order of the elements in a set is unimportant. While representing a set in roster form, the elements are generally not repeated. Only distinct elements are written while representing a set in roster form. Set-builder form The set-builder form is a more concise form of a given set. To write the set in the set-builder form, start with a bracket and write the variable. Then a colon is placed and a property is assigned to this number. Ex 1: {2, 3, 5 and 7} is written in set-builder form as P = {x:x is a prime number, x < 10}. The set is named as P and read as P is the set of all x such that x is a prime number less than 10. Ex 2: Represent the set of natural numbers between 20 and 30 using the set-builder form. Set of natural numbers between 20 and 30 = {21, 22, 23, 24, 25, 26, 27, 28, 29} We name this set A. A = {n:n is a natural number, 20 < n < 30} This is read as: A is the set of all n such that n is a natural number and n is lies between 20 and 30.

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