Here you will learn what is an empty set in math, its symbol and definition with examples.
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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 the symbol \(\phi\).
In Roster method, \(\phi\) is denoted by { }.
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.
Example 1 : { x \(\in\) R : \(x^2\) = -1 } = \(\phi\)
Example 2 : 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.
A set consisting of atleast one element is called a non-empty or non-void set.
Note : 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 \(\phi\).
Note : The power set of an empty set has only one element i.e. P(A) = {\(\phi\)}.
