Question

Give the example of a set which contains only one subset which is an improper subset.

Answer 1

To solve this question, we should have a lot of information about the sets, the subsets, and improper subsets. Sets are one of the most important topics in Mathematics. According to the question, we need to first check which set contains a single subset and the subset should also be an improper subset.

Complete answer:
As said earlier, we should have a whole lot of information about the sets. A set is a group or collection of elements, enclosed within brackets. The elements in the sets can be anything, either names, numbers, alphabets, or even other types of sets. We have to always assign a variable in capital letter form to every set.
Now, we will see what subsets are. Subsets are basically a small version of sets only. If the elements of $A$ are the same as the elements of $B$, then we can say that, $A$is the subset of $B$. There are many types of subsets in Mathematics.
If we say that $A$ is having all the elements which are in $B$, which means that $A$ is a subset of $B$, but $A$ is not equal to $B$, then $A$ is known to be a proper subset of $B$.
If we say that $A$is having all the elements which are in $B$, and $A$ is equal to $B$, then $A$ is an improper subset of $B$.
Now, if we look here, then we can see that the set contains only a single subset, and it is also an improper subset, then it will be a null set. Therefore, the example of a set containing only one subset which should be an improper subset is the null subset.

Note:
Null set is known to be the empty set in Set Theory of Mathematics. It is the set that contains no elements. It is empty. It just has the brackets outside, but no elements inside. The symbol of a null can be.