What is the total number of subsets that can be formed from a set containing six elements, including both the empty set and the set itself?

To determine the total number of subsets that can be created from a set with n elements, we use the formula:

• Number of subsets = 2ⁿ

In our case, since we have a set containing six elements, we can substitute n with 6:

• Number of subsets = 2⁶ = 64

This calculation means that there are a total of 64 subsets possible from a set with six elements. These subsets range from the null set (or empty set) to the set itself containing all six elements.

To further break it down:

• The null set is one of these subsets.
• All combinations of elements in various sizes are included, for example, subsets with one element, two elements, and so on up to the full set of six elements.

Hence, the complete list of all subsets is represented as follows:

• 1 subset with 0 elements (the null set)
• 6 subsets with 1 element
• 15 subsets with 2 elements
• 20 subsets with 3 elements
• 15 subsets with 4 elements
• 6 subsets with 5 elements
• 1 subset with 6 elements (the set itself)

In summary, from a single set containing six elements, you can form a total of 64 subsets, encompassing all possible combinations including both the empty set and the complete set.