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Examples 2.2.4(a):

If S = {1,2,3}, then what is P(S) ? What is the power set of the set S = {1, 2, 3, 4} ? How many elements does the power set of S = {1, 2, 3, 4, 5, 6} have ?
The power set is the set of all subsets of a given set.

For the set S = {1,2,3} this means:

Hence: Therefore, we have: For the set S = {1,2,3,4} this means: Therefore, we have:

Finally, if S = {1,2,3,4,5,6} then, based on the above examples, we would suspect that

In fact, if a set S contains n elements, then its power set will contain 2n elements. This can be proved by induction as an exercise.
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