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 = 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.
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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}
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}
