Question

what is the difference between proper set and power set? with an example

Answer 1

A subset is a collection of “some” of the elements of a set (“some” could be none or all as well). The power set is the collection of ALL subsets of a set.

Ex.

Let S = {1, 2, 3}

Here is an example of a subset of S: {2, 3}.

There is only one power set of S, and the above subset will be one of the elements of this power set.

P(S) = { { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} }.