> For the complete documentation index, see [llms.txt](https://veriny.gitbook.io/berkeley/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://veriny.gitbook.io/berkeley/discrete-mathematics/set-notation.md).

# Sets + Mathematical Notation

A dictionary of mathematical notation.

| Term          | Symbol           | Meaning                                                                                                                                                                                | TEX           |
| ------------- | ---------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------- |
| Subset        | $$\subseteq$$    | If every element of $$A$$ is in $$B,$$ we say that $$A \subseteq B.$$                                                                                                                  | `\subseteq`   |
| Proper Subset | $$\subset$$      | If every element of $$A$$ is in $$B,$$ but the two sets are guaranteed to not be equal, we say that $$A \subset B.$$                                                                   | `\subset`     |
| Intersection  | $$\cap$$         | Used to denote the set of elements that are shared between two sets. $$A\ \cap\ B$$ denotes the set containing elements shared between $$A$$ and $$B.$$                                | `\cap`        |
| Union         | $$\cup$$         | Used to denote the set that contains all elements of one or many sets, whether they are shared or not. $$A\ \cup\ B$$denotes the set containing elements contained in $$A$$ and $$B.$$ | `\cup`        |
| Complement    | $$^\complement$$ | Used to denote items that are in one set but not the other. $$A^\complement B$$ is the set of elements that are contained in $$A$$but not in $$B.$$                                    | `\complement` |
| Cross Product | $$\times$$       | Used to denote the set of pairs those first component is in $$A$$and whose second is in$$B.$$                                                                                          | `\times`      |
| In            | $$\in$$          | Used to show an item is in a set.                                                                                                                                                      | `\in`         |
| Not In        | $$\notin$$       | Used to show an item is not in a set.                                                                                                                                                  | `\notin`      |
| Conjunction   | $$\wedge$$       | $$P\ \wedge \ Q$$ is true if both $$P$$and$$Q$$are true.                                                                                                                               | `\land`       |
| Disjunction   | $$\lor$$         | If either $$P$$and$$Q$$are true, then $$P\ \lor \ Q$$is true.                                                                                                                          | `\lor`        |
| Set           | $${}$$           | Used to denote a set.                                                                                                                                                                  | `\{\}`        |
| Implies       | $$\implies$$     | $$P \implies  Q$$ states that $$P$$ being true means $$Q$$is true. Doesn't give any info about what happens when $$P$$is false.                                                        | `\implies`    |
| Iff           | $$\iff$$         | If and only if.                                                                                                                                                                        | `\iff`        |
| For all       | $$\forall$$      | Used to refer to all of the elements within a specific set.                                                                                                                            | `\forall`     |
| There exists  | $$\exists$$      | Used to declare the existance of one or more of something.                                                                                                                             | `\exists`     |
| Negation      | $$\neg$$         | $$\neg P$$ is true when $$P$$is false.                                                                                                                                                 | `\neg`        |