Power set

Imagine you have a toy box with 3 toys inside - a teddy bear, a car, and a ball. Now, the grown-ups call this toy box a set.

A power set is like making a new toy box containing ALL the possible combinations of toys you can make from the original toy box.

So, the power set of our 3-toy box would contain the original set, plus all the possible combinations of toys. Here's what it would look like:

- The original set: {teddy bear, car, ball}
- Sets with 2 toys: {teddy bear, car}, {teddy bear, ball}, {car, ball}
- Sets with 1 toy: {teddy bear}, {car}, {ball}
- The empty set: {}

Notice that the power set also includes the empty set - this is because having no toys is still a possible option.

So, the power set of any set is like making a new set that includes the original set and all the possible subsets (sets with some of the original elements) of the original set.