# Sets + 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` | --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://veriny.gitbook.io/berkeley/discrete-mathematics/set-notation.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.