Question

Classify the following set into the empty set, finite set, or infinite set. In the case of a finite set, find the cardinal number.

$\left\{x:x\text{is a prime factor of}36\right\}$

Answer 1

Prime factor:

Empty Set: The set containing no elements is called an empty set or null set. It is written as {} or ф.

Finite sets: A set whose elements can be counted is called a finite set. Examples: $A=\left\{1,2,3,\dots ,60\right\}$

Infinite sets: A set that has an uncountable number of different elements is called an infinite set. Example: $N=1,2,3,\dots$

Cardinal numbers of a set: The number of distinct elements in a finite set is called the cardinal number of the set. The cardinal number of a finite set is denoted by n(A).

Example: $B=1,2,3,\dots ,10$ has 10 elements , so $n\left(B\right)=10$.

Now,

$x$ is a prime factor of $36$

$36=2^2\times 3^2$

So, prime factor are $2,3$

It is a finite set. its elements are $\left(2\right)$ and $\left(3\right)$

$n\left(A\right)=2$

Hence, it is a finite set and cardinal number is $2$