There are four elements in the set. Each element will be in a given subset, or not. There are these two possibilities for each of the four elements, so a total of 2^4 =

If all elements are out, it is called the "empty set", which is a subset of every set. If all elements are in you have

_____

One way to list the subsets is to make a list of the binary numbers between 0 and 15. These will look like

0000, 0001, 0010, 0011, 0100, 0101, ..., 1101, 1110, 1111

Every place there is a 1 in a number, add the corresponding element to the subset. The first three correspond to

{ }, {8}, {6}, ...

and the last two correspond to

{2, 4, 6}, {2, 4, 6, 8}

**16 different subsets**.If all elements are out, it is called the "empty set", which is a subset of every set. If all elements are in you have

**p**itself. It is called an "improper subset," but**p**is still a subset of**p**._____

One way to list the subsets is to make a list of the binary numbers between 0 and 15. These will look like

0000, 0001, 0010, 0011, 0100, 0101, ..., 1101, 1110, 1111

Every place there is a 1 in a number, add the corresponding element to the subset. The first three correspond to

{ }, {8}, {6}, ...

and the last two correspond to

{2, 4, 6}, {2, 4, 6, 8}