{"id":9493,"date":"2022-01-15T20:26:14","date_gmt":"2022-01-15T14:56:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9493"},"modified":"2022-01-16T17:15:30","modified_gmt":"2022-01-16T11:45:30","slug":"empty-set-null-or-void-set-in-math-symbol-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/empty-set-null-or-void-set-in-math-symbol-examples\/","title":{"rendered":"Empty Set (Null or Void Set) in Math – Symbol and Examples"},"content":{"rendered":"
Here you will learn what is an empty set in math, its symbol and definition with examples.<\/p>\n
Let’s begin –<\/p>\n
What is the Empty Set in Math ?<\/h2>\n
Definition<\/strong> : A set is said to be empty set if it has no element. It is also called null or void set.<\/p>\n
It is denoted by the symbol \\(\\phi\\).<\/p>\n
In Roster method, \\(\\phi\\) is denoted by { }.<\/p>\n
It follows from the definition that a set A is an empty set if the statement x \\(\\in\\) A is not true for any x.<\/p>\n
Example 1<\/strong><\/span> : { x \\(\\in\\) R : \\(x^2\\) = -1 } = \\(\\phi\\)<\/p>\n
Example 2<\/strong><\/span> : The set A given by A = { x : x is an even number greater than 2 } is an empty set because 2 is the only even prime number.<\/p>\n
A set consisting of atleast one element is called a non-empty or non-void set.<\/p>\n
Note<\/strong> : If A and B are any two empty sets, then x \\(\\in\\) A iff (if and only if) x \\(\\in\\) B is satisfied because there is no element x in either A or B to which the condition may be applied. Thus A = B. Hence, there is only one empty set and we denote it by \\(\\phi\\).<\/p>\n
Note<\/strong> : The power set of an empty set has only one element i.e. P(A) = {\\(\\phi\\)}.<\/p>\n","protected":false},"excerpt":{"rendered":"
Here you will learn what is an empty set in math, its symbol and definition with examples. Let’s begin – What is the Empty Set in Math ? Definition : A set is said to be empty set if it has no element. It is also called null or void set. It is denoted by …<\/p>\n