{"id":3661,"date":"2021-08-05T23:43:12","date_gmt":"2021-08-05T23:43:12","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3661"},"modified":"2022-01-15T21:02:46","modified_gmt":"2022-01-15T15:32:46","slug":"types-of-sets-mathematics","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/types-of-sets-mathematics\/","title":{"rendered":"Types of Sets Mathematics"},"content":{"rendered":"

Set is defined as a collection of objects. There are many types of sets in mathematics which are given below.<\/p>\n

Types of Sets<\/h2>\n

1). Empty Set<\/h3>\n

A set is said to be empty or null or void set<\/a> if it has no element and it is denoted by \\(\\phi\\).<\/p>\n

for example<\/span> : The set A is given by A = [ x : x is an even prime number greater than 2 ] is an empty set because 2 is the only even prime number.<\/p>\n

2). Singleton Set<\/h3>\n

A set consisting of a single element is called a singleton set.<\/p>\n

for example<\/span> : The set {5} is a singleton set.<\/p>\n

3). Finite Set<\/h3>\n

A set is called finite set if it is either void set or its element can be listed by the natural numbers 1, 2, 3 ….. n for any natural number n.<\/p>\n

for example<\/span> : The set of even natural numbers less than 100.<\/p>\n

4). Infinite Set<\/h3>\n

A set whose elements cannot be listed by the natural numbers 1, 2, 3 ….. n for any natural number n is called infinite set.<\/p>\n

for example<\/span> : The set of all points in a plane.<\/p>\n

5). Equivalent Sets<\/h3>\n

Two finite sets A and B are said to be equivalent if their cardinal numbers are same i.e. n(A) = n(B).<\/p>\n

for example<\/span> : If A = { 1, 2 } and B = { 3, 4 }, both are equivalent as cardinality of A is equal to the cardinality of B. i.e. |A| = |B| = 2.<\/p>\n

6). Equal Sets<\/h3>\n

Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.<\/p>\n

If sets A and B are equal, we write A = B and A \\(\\ne\\) B when A and B are not equal.<\/p>\n

for example<\/span> : If A = { 1, 2, 5, 6 } and B = { 5, 6, 2, 1 }, then A = B, because each element of A is an element of B and vice versa.<\/p>\n

7). Subsets<\/h3>\n

Let\u00a0 A and B be two sets. If every element of A is a element of B, then A is called a subset of B.<\/p>\n

If A is a subset of B, we write A \\(\\subset\\) B, which is read as “A is a subset of B”.<\/p>\n

for example<\/span> : If A = { 1 } and B = { 3, 2, 1 }, then A \\(\\subset\\) B, because every element of A is an element of B.<\/p>\n

8). Universal Set<\/h3>\n

A set that contains all sets in a given context is called universal set.<\/p>\n

for example<\/span> : when we are using sets containing natural numbers, then N is the universal set.<\/p>\n

9). Power Set<\/h3>\n

Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A).<\/p>\n

Since the empty set and set A itself are subsets of A and are therefore elements of P(A). Thus the power set of a given set is always non-empty.<\/p>\n

for example<\/span> : Let A = {1, 2}. Then the subsets of A are :<\/p>\n

\\(\\phi\\), {1}, {2}, {1, 2}<\/p>\n

Hope you learnt types of sets in mathematics , learn more concepts of sets\u00a0 and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – Operation of Sets \u2013 Formula of Sets in Math<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What is Sets in Mathematics \u2013 Methods to write a Set<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Set is defined as a collection of objects. There are many types of sets in mathematics which are given below. Types of Sets 1). Empty Set A set is said to be empty or null or void set if it has no element and it is denoted by \\(\\phi\\). for example : The set A …<\/p>\n

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