Question

List all the subsets of the following sets. $$ \\{1,2,3,4\\} $$

Short answer

The subsets are: {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, and {1, 2, 3, 4}.

Step-by-step solution

Find Subsets Containing Zero Elements

Start by listing the subset that contains no elements. This is called the empty set. It is represented by {}. There is always one subset that contains no elements, regardless of the size of the original set.

Find Subsets Containing One Element

Next, find all subsets that contain only one element. To do this, simply list each element in the original set as its own separate subset. For our given set, these subsets are: {1}, {2}, {3}, {4}.

Find Subsets Containing Two Elements

Now, list all subsets containing two elements. Do this by pairing each element in the original set with every other element. For our set, these subsets are: {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}.

Find Subsets Containing Three Elements

By combination each element with the others, the subsets containing three elements are: {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}.

Find Subsets Containing Four Elements

Finally, the given set itself is a subset that includes four elements: {1, 2, 3, 4}.