Subsets in Set Theory

A detailed tutorial on how to identify subsets of a set. Step by step tutorial including several examples of how to find subsets in a set for reference.

Each set in set theory has a certain amount of subsets. There is an easy way figure out how many subsets a set has. Pretend that every element of a set is 2, and multiply them together. This will be your number of subsets. For example, if you have three elements, you will have 8 subsets, because 2 cubed (which is 2 to the power of 3, or 2 times 2 times 2) is equal to 8. Now that you have determined how many subsets there are, you have to figure out what they are. A subset is defined as any set containing all or part of a set. Two subsets are going to be the set itself, and an empty set. Sometimes they are your only subsets. Now, following the definition, a subset must be all possible sets. This means, sets of one element - one for each element in your set. In addition to that, you may have sets of two elements – one for each possible combination of elements in your set. This should be continued until you have reached the maximum number of elements in the set you atarted out with.