Bat-Batman or Batman-bat?

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How about a discussion about sets and subsets? These are interesting concepts given the possibility of generalizing them in other aspects of everyday life. Its definition is quite simple, a set is a collection of elements, while a subset is a collection of elements within another collection of elements. For example, this blog is a collection of the elements posts and pages. The posts form a subset of the blog.

This reasoning can be extended to more varied aspects, for example the set of words in the Portuguese language, within this, we have the subsets of verbs, adjectives, pronouns, prepositions. If something belongs to the subset then it also belongs to the set. So verbs are not prepositions, but verbs are words, just as prepositions are not verbs but prepositions are words.

We can also have several levels of disjoint subsets, for example in biology, the domestic dog belongs to the Canids group, which belongs to the Mammals group which belongs to the Animal Kingdom group. The wolf, despite not belonging to the domestic dog group, belongs as well as the domestic dog to the Canids group. The cat, despite not belonging to the Canids group, belongs to the Mammals group. Although the penguin does not belong to the set of Mammals, it belongs to the set of the Animal Kingdom.

These are relationships that we can build from diverse and unique aspects, such as the set of flying animals. The hawk belongs to the group of flying animals, but not every bird belongs to this group. In the same way that the bat belongs to the group of flying animals, but it is not a bird. The set of birds and mammals is disjoint, that is, they do not share any elements that are mammal and bird. Thus, the set of flying animals fears elements of the set of birds and mammals, but both have an empty intersection, since no element is at the same time in the set of mammals and birds.

In an episode of The Big Bang Theory (season 9, episode 21, The Combustion Sight Party), they discuss the term Batman being used for a human being dressed up as a bat, and the term in the same sequence of comic stories , Man-bat be used for a human being turned into a bat. And then follow the rationale for what the term should be if Man-bat dressed up as a bat? If we organize this problem in set diagrams, we will obtain a situation like the figure below. In which the term bat appears before the name if the subject is dressed as a bat.

Other analyzes can be performed, but they are difficult to represent from set diagrams. We will try to do it in a more descriptive way:

Name rules:

Bat Being

Bat

Human Being

Man

Bat costume

Insert Bat before name

Human costume

Insert Man before name

Become a bat

Insert -bat after the name

Become human

Insert -man after the name

With these syntax rules, we define 16 initial cases derivable from their combinations, as listed below:

1. Bat that became human: Bat-man;

2. Bat that became a bat: Bat-bat;

3. Bat that dresses as a human: Manbat;

4. Bat dressed as bat: Batbat;

5. Bat that became human and dressed as human: Manbat-man;

6. Bat that became human and dresses as a bat: Batbat-man;

7. Bat that became a bat and dresses up as a bat: Batbat-bat;

8. Bat that turned into a bat and dresses as a human: Manbat-bat.

9. Human who became human: Man-man;

10. Human turned bat: Man-bat;

11. Human dressed as human: Manman;

12. Human dressed as a bat: Batman;

13. Human who became human and dresses as a human: Manman-man;

14. Human who became human and dresses as a bat: Batman-man;

15. Human who became a bat and dresses up as a bat: Batman-bat;

16. Human who became a bat and dresses as a human: Manman-bat.

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