We saw that the three-element set above had 8 = 2 subsets. In general, a set with n elements has 2n subsets, as can be seen in the following manner. We form subsets P of U by considering each of the elements of U in turn and deciding whether or not to include it in the subset P. If we decide to put every element of U into P, we get the universal set, and if we decide to put no element of U into P, we get the empty set. In most cases we will put some but not all the elements into P and thus.
