Question

The cardinal number of the empty set is
\[\left( a \right){\text{ 2}}\]
\[\left( b \right){\text{ 1}}\]
\[\left( c \right){\text{ 0}}\]
\[\left( d \right){\text{ None of these}}\]

Answer 1

Hint: So for answering this question, we have to know about the cardinal number. Cardinal numbers are those numbers having distinct elements in a finite set. It is generally denoted by $n\left( A \right)$ and it can be read as the number of elements in the set.

Complete step-by-step answer:
As in the question it is given that there is an empty set which means there will not be any element in that set. And mathematically it can be written as
Set $A = \left\{ {} \right\}$
Since there is no element in the set. Therefore, we can say that the cardinal number of set $A = 0$ and it will be written as $n\left( A \right) = 0$
Hence, the option $\left( c \right)$ is correct.

Additional information:
There are mainly three different forms of numbers, the first one cardinal number. The second one is the ordinal number. So ordinal numbers are those numbers which tells us the position of something in the list.
And the last form is nominal numbers. So the nominal numbers are those numbers which are used only as a name or we can say to identify something. Which will not be as actual value or position.
For example, if a figure showing the car and the number of the car is $6$ and the car number $99$ has a red roof and it is at ${1^{st}}$ position. Then $6$ will be the cardinal number and ${1^{st}}$ will be the ordinal number and $99$ will be the nominal number.

Note: In the cardinal number, if the set is infinite then the cardinal number is not defined. So we can say that the cardinal number of an empty set will be equal to zero. It does not have fractions or decimals, it is only used for counting.