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If the universal set, U, has N elements then it has 2N subsets.
For example, if you take the set A = {1, 2}, then the following sets are all subsets of it: {}, {1}, {2}, {1, 2}. That is, all the sets that fulfill the condition that all of its elements are also elements of the set "A".
If tiu have a set S, its power set is the set of all subsets of S (including the null set and itself).
Once example is the whole numbers and subsets are the numbers 1,2 and 3 written {1,2,3}. Another example is all the colors. Subsets would be any number of individual colors. The universal set may be finite or infinite.
If set A is a subset of set B, that means that all elements in set A are also in set B. In the case of a proper subset, there is the additional specification that the two sets are not equal, i.e., there must be an element in set B that is not also an element of set A.