{"id":7614,"date":"2022-04-15T17:47:46","date_gmt":"2022-04-15T12:17:46","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7614"},"modified":"2025-06-02T20:50:44","modified_gmt":"2025-06-02T15:20:44","slug":"what-are-sets-and-their-types%ef%bf%bc","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-sets-and-their-types%ef%bf%bc\/","title":{"rendered":"What are sets and their types?\ufffc"},"content":{"rendered":"\n

Introduction<\/strong>– The concept of sets is widely used in mathematics as well as in other fields such as engineering, computer sciences etc.<\/p>\n\n\n\n

The whole structure of Pure or Abstract Mathematics is based on the concept of sets.<\/p>\n\n\n\n

German mathematician Georg Cantor (1845-1918) introduced and developed the theory of sets and subsequently many branches of modern Mathematics have been developed based on this theory.<\/p>\n\n\n\n

Sets<\/strong><\/h2>\n\n\n\n

A set is a collection of well-defined objects which are called the elements or members of the set.<\/p>\n\n\n\n

Here by well defined means, given a particular collection of objects as a set and a particular object, it must be possible to determine whether that particular object is a member of the set or not.<\/p>\n\n\n\n

We generally use capital letters to denote sets and lowercase letters for elements.<\/p>\n\n\n\n

Suppose an element \u2018a\u2019 is from a set X, then we represent it as- <\/p>\n\n\n\n

Which means the element \u2018a\u2019 belongs to the set X.<\/p>\n\n\n\n

If the element is not form the group then we use \u2018not belongs to\u2019.<\/p>\n\n\n\n

Representation of sets<\/strong><\/h2>\n\n\n\n

Sets are represented in the following two methods :<\/p>\n\n\n\n

1. Roster or tabular method<\/p>\n\n\n\n

2. Set-builder or Rule method<\/p>\n\n\n\n

Roster or tabular method – In this way, the elements of the set are separated by comma and contained in the bracket-{  }.<\/p>\n\n\n\n

Example: A = {2, 3, 5, 7, 11, 13}<\/p>\n\n\n\n

B = {1, 3, 5, 7, …}<\/p>\n\n\n\n

Set-builder or Rule method<\/strong><\/p>\n\n\n\n

The second way is that we define the characteristic of the element.<\/p>\n\n\n\n

For example-<\/p>\n\n\n\n

Suppose we have a set \u2018A\u2019 of all odd integers which are greater than 3.<\/p>\n\n\n\n

Then we can represent it as-<\/p>\n\n\n\n

A = {x | x is an odd integer, x>3 }<\/p>\n\n\n\n

Subsets<\/strong><\/h2>\n\n\n\n

Let every element of set X is also an element of a set Y, then X is said to be the subset of Y.<\/p>\n\n\n\n

Symbolically it is written as-<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Which is read as- X is the subset of Y.<\/p>\n\n\n\n

Note- If X = Y then <\/p>\n\n\n\n

Proper sub-set<\/strong><\/h2>\n\n\n\n

A set X is called proper subset the set Y is-<\/p>\n\n\n\n

1. X is subset of Y<\/p>\n\n\n\n

2. Y is not subset of X<\/p>\n\n\n\n

Note- every set is a subset to itself.<\/p>\n\n\n\n

Equal sets-<\/strong><\/h2>\n\n\n\n

If X and Y are two sets such that every element of X is an element of Y and every element of Y is an element of X, the set and set Y will be equal always.<\/p>\n\n\n\n

We write it as X = Y and read as X and Y are identical.<\/p>\n\n\n\n

Super set-<\/strong><\/h2>\n\n\n\n

If X is a subset of Y, then Y is called a super set of X.<\/p>\n\n\n\n

Null set-<\/strong><\/h2>\n\n\n\n

A set which does not contain any element is known as null set.<\/p>\n\n\n\n

We denote a null set by \u2205<\/p>\n\n\n\n

The null set is a subset of every set.<\/p>\n\n\n\n

Singleton-<\/strong><\/h2>\n\n\n\n

A set which has only one element is called singleton.<\/p>\n\n\n\n

Example- A = {10} and B = {\u2205}<\/p>\n\n\n\n

Finite and infinite sets:<\/strong><\/h2>\n\n\n\n

Definition: A set containing finite number of distinct elements so that the process of counting the elements comes to an end after a definite stage is called a finite set; otherwise, a set is called an infinite set.<\/p>\n\n\n\n

Example: State which of the following sets are finite and which are infinite.<\/p>\n\n\n\n

(i) the set of natural numbers N \u2013 infinite set<\/p>\n\n\n\n

(ii) the set of concentric circles in a plane-  infinite set<\/p>\n\n\n\n

(iii) the set of rivers on the earth- finite set<\/p>\n\n\n\n

Equal sets:<\/strong><\/h2>\n\n\n\n

Definition : Two sets A and B are equal sets if every element of A is an element of B and every element of B is also an element of A. In other words, A is equal to B, denoted by A = B if A and B have exactly the same elements. If A and B are not equal, we write .<\/p>\n\n\n\n

Power set:<\/strong><\/p>\n\n\n\n

Definition : The set consisting of all the subsets of a given set A as its elements, then we call it the power set of A and is denoted by P(A) . Thus,<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

The concept of sets is widely used in mathematics as well as in other fields such as engineering, computer sciences etc.<\/p>\n","protected":false},"author":3,"featured_media":7117,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7614","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"\nWhat are sets and their types?\ufffc - Goseeko blog<\/title>\n<meta name=\"description\" content=\"The concept of sets is widely used in mathematics as well as in other fields such as engineering, computer sciences etc.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/what-are-sets-and-their-types\ufffc\/\" \/>\n<meta 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