# Cardinality of a Set

## Definition of Cardinality of a Set

A set may contain a single element or multiple elements. The sets having multiple elements may be countable or uncountable. In other words, a set may contain a definite number of elements or an indefinite number of elements. The Cardinality of a Set is basically the count of the number of elements present in the set.

Therefore, the Cardinality of a Set may be defined as the size of the set or the number of elements present in the set.

For example, if the number of elements present in a set is $5$, then the Cardinality of the Set will be $5$.

The Cardinality of an Empty set is $0$ and the Cardinality of an Infinite Set is not defined.

## Symbol for Cardinality of a Set

Let us consider two sets $A$ and $B$ as shown in the figure below.

The set $A$ has $5$ elements, i.e.,

$A=\{1, 2, 3, 4, 5\}$

The Cardinality of the Set $A$ can be written as

$n(A)=5$

Also, as shown in the figure, set $A$ and $B$ has the same number of elements. For each element in set $A$, there is one element present in set $B$. Therefore, it can be said that the set $A$ and $B$ have same Cardinality.

$\therefore$ $n(A)=n(B)=5$

### What is Cardinality of a set?

The cardinality of a set is the size of the set or the number of elements present in the set.

### What is the symbol for Cardinality of set?

The cardinality of a set A is denoted by n(A). For example, if set A has 7 elements then the cardinality of the set is n(A)=7.

### How do you find the cardinality of a set?

The cardinality of a set is basically the number of elements present in the set. To find the Cardinality of a Set, first, find the number of elements present in it.

For example, if a set A has 10 elements then the cardinality of the set A is n(A)=10.

It is to be noted that, the Cardinality of an Empty set is always 0 and the Cardinality of an infinite set is not defined.

### What is the cardinality of Set A and Set B?

If set A and set B has the same cardinality then it can be said that both the sets have the same number of elements even if the sets have different elements or there is a one-to-one correspondence between set A and set B.

### What is the cardinality of an Empty set?

The cardinality of an Empty set is 0 because an Empty Set has no elements.

### How do you prove two sets have the same cardinality?

To prove whether two sets have the same cardinality we have to find the number of elements present in both sets. If the number of elements in both sets is equal then both the sets will have the same cardinality.