Once upon a time there was a magical world called the Universe. In this world, everything was made up of sets. A set is a collection of things, like the set of all animals, or the set of all colors.

One day, a group of sets decided they wanted to become more powerful, so they joined together to form a poset. A poset is a set with some extra rules about which sets are bigger or smaller than others.

The poset was very proud of its powerset. The powerset of a set is all the possible subsets of that set. For example, the powerset of the set of all animals would be the set of all possible combinations of animals, like the set of just cats, or the set of just dogs and cats.

One day, a subset of the poset had an idea. They wanted to see if they could find a superset that contained all of the sets in their poset. A superset is a set that contains all the elements of another set. The subset searched far and wide and finally found the perfect superset. It was the union of all the sets in the poset.

The union of two sets is a new set that contains all the elements of both sets. For example, if you have the set of all cats and the set of all dogs, the union of those sets would be the set of all animals.

The subset and the superset were very happy together, and they lived happily ever after. And that’s the story of sets, subsets, supersets, posets, powersets, unions, and the universe.

The end.

Reflections

1. What is a set?
2. What is a poset?
3. What is the powerset of a set?
4. What is a subset?
5. What is a superset?
6. What is a union of sets?
7. How does the poset in the story become more powerful?
8. Why did the subset in the story search for a superset?