Typing Logical Symbols

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# Typing Logical Symbols

Author: Billy Price

This is a small glossary of symbol-commands for $\mathrm{\LaTeX}$, specifically the math-environment, which can be used in Microsoft’s equation editor in OneNote and Word.

### OneNote/Word Usage

Unfortunately, equation editing is only supported in the desktop app version of OneNote - not the webapp embedded into Microsoft Teams. You can download the free desktop app here, and open your shared notebook by choosing “Open in app” from your notebook in Teams.

To enter equation mode in OneNote use the keyboard shortcut

• ctrl + = on Mac
• alt + = on Windows.

## Common Symbols

To lookup any symbol not listed here, use Detexify.

Propositional Logic

• $\bot$ - \bot
• $\top$ - \top
• $\neg$ - \neg
• $\wedge$ - \wedge
• $\vee$ - \vee
• $\Rightarrow$ - \Rightarrow
• $\Leftrightarrow$ - \Leftrightarrow
• $\oplus$ - \oplus
• $\equiv$ - \equiv
• $\not\equiv$ - \not\equiv
• $\vDash$ - \vDash or \models
• $\nvDash$ - \nvDash
• $\varphi$ - \varphi
• $\psi$ - \psi

Predicate Logic

• $\forall$ - \forall
• $\exists$ - \exists

Set Notation

• $\mapsto$ - \mapsto
• $\emptyset$ - \emptyset
• $\in$ - \in
• $\cup$ - \cup
• $\cap$ - \cap
• $\subseteq$ - \subseteq
• $\setminus$ - \setminus
• $\{ \}$ - \{ \}

The backslash is necessary in front of each curly-brace, since by themselves they are used to group latex expressions.

### Examples

• $\forall x \exists y L(x,y)$ - \forall x \exists y L(x,y)
• $(X \cup Y) \setminus \{P, \neg P\}$ - (X \cup Y) \setminus \{P, \neg P\}
• $\varphi_1, \varphi_2, \varphi_3 \vDash \psi$ - \varphi_1, \varphi_2, \varphi_3 \vDash \psi