Question

List all the subsets of the following sets. $$ \\{\varnothing\\} $$

Short answer

The subsets of the set {∅} are {} and {∅}.

Step-by-step solution

Identify the elements in the set

The set given is {∅}. This set has only one element and that element is the empty set.

List all subsets with no elements

A subset of a set can have zero elements. In this case, the subset with no elements is the empty set, represented as {}. This is a subset of all sets, including our given set.

List all subsets with one elements

A subset of a set can have one element. In this case, it is the element that the original set contains. Therefore, the subset of {∅} with one element is {∅} itself.