Question

List all the subsets of the following sets. $$ \\{1,2, \varnothing\\} $$

Short answer

The subsets of the set \{1,2,\varnothing\} are: \{\}, \{1\}, \{2\}, \{\varnothing\}, \{1,2\}, \{1,\varnothing\}, \{2,\varnothing\} and \{1,2,\varnothing\}.

Step-by-step solution

Identify the sets

The first step is to list out all elements of the set. In this case, the set is \{1,2,\varnothing\}.

Write down all possible subsets

Then, write down all the subsets of the set. A subset can contain any number of elements from the set, including none of the elements and all of the elements. Here are all possible subsets: \{\}, \{1\}, \{2\}, \{\varnothing\}, \{1,2\}, \{1,\varnothing\}, \{2,\varnothing\}, and \{1,2,\varnothing\}.

Check for validity

The last step is to make sure all subsets listed are actually subsets. All elements in each subset should appear in the original set. Upon checking, it looks like every subset listed does satisfy this condition.