Empty Set

Definition of Empty Set

An Empty Set or Null Set may be defined as a unique set that has no elements in it. Therefore, the size of an Empty Set is zero (0) as it has no elements present. Also, the Cardinality of an Empty Set or Null Set is Zero (0).

An Empty Set sometimes is also referred to as a Null set.

Symbol of Empty Set

The Empty Set or Null Set is denoted by the Greek letter . An Empty Set or Null Set can also be represented by \{\}.

Properties of an Empty Set

The Properties of an Empty Set are discussed below:

  • The number of elements in an Empty set is Zero (0).
  • An Empty Set is a Subset of any set A.
  • The Union of an Empty set with any set A is the set A itself.

Therefore, A ∪ \phi =A

  • The Intersection of an Empty Set with any set A is an Empty Set.

Therefore, A ∩ \phi =\phi

  • The Cartesian product of an Empty Set with any set A is an Empty set.
  • The only subset of an Empty Set is the Empty Set itself.

Example of Empty set

Some examples of Empty set is described below.

  • The set of Prime Numbers between 7 and 11.

There are 3 numbers between 7 and 11. Those are 8, 9 and 10. None of these numbers is Prime. Therefore, the set of Prime Numbers between 7 and 11 is an Empty Set or Null Set.

  • The set of Natural Number which are less than 1.

We know that the set of Natural Numbers starts from 1 and ends at +\infty. Therefore, there is no Natural Number that is less than 1. Hence, the set of Natural Numbers that are less than 1 is an Empty Set or Null Set.

  • The Set of Prime Number which are less than 2.

Similarly, there is no Prime Number that is less than 2 as 2 is the smallest Prime Number. Therefore, the set of Prime Number which is less than 2 is an Empty Set or Null Set.

Frequently Asked Questions (FAQ)

The set that does not contain any element is called an Empty set or null set. An empty set is denoted by the Greek letter ∅.

The size of an empty set is 0.

Yes, ∅ is an empty set.

The empty set is a set that has no elements in it. An empty set is denoted by the Greek letter ∅.
The example of an Empty Set is the set of the months in a year that has 32 days. Since there is no month that has 32 days, therefore, the above Set does not have any element and hence called an Empty Set.

The intersection of an empty set with another set results in an empty set.

The union of an Empty set with any set A is set A itself.

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