What is an Empty Set or Null Set?

A short tutorial that explains the definition of empty set with example.

Elementary Set Theory

Empty set is also referred as Null set. It is a set without any elements. Typically, a set refers to the collection of individual elements. The empty set is represented by the open and closed curly braces symbol as shown { }. Alternatively the symbol "Ø "(known as minuscule) is also used to refer the Empty set. The below tutorial explains elementary set theory and what is an empty set or null set.
What Is An Empty Set
Cardinality
Cardinality refers to the total number of elements in a set. For example, consider the set of vowels. Let it be called as Set A.
Hence, Set A = {a, e, i, o, u}
Its has a cardinality of 5, as the set A has five elements in it. It can be written as,
|A| = 5

Cardinality of the Empty Set
The Cardinality of the empty set is Zero as the set contains no elements. Using proper set notation, we can write down as
|Ø| = 0
Empty Set Notation
Practical Example of Empty Set
The set of cows with 10 legs.
The set of numbers that is both even and odd.
Example:
Mathematically, lets consider an example. Find A intersection B (A ∩ B).
A = {m, n, o, p}
B = {d, y, v, e}
Intersection of the two set is about finding the elements that are present in both the set A and B.
Here in the given example, the intersection of A and B is none. So we can write it down as
A ∩ B = { }.
Empty Set Example


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