Logical Or in LaTeX (\lor)

Where it is used

Logical OR (disjunction), true when at least one operand is true.

\lor is an alias of \vee, used in propositional and predicate logic: p \lor \neg p is the law of excluded middle. LaTeX spaces it as a binary operator, so p \lor q needs no manual spacing commands. For many disjuncts, \bigvee_{i} p_i is the large operator. Exclusive or is a different symbol: \oplus or \veebar. Boolean algebra and circuit design often write OR as +. Prefer \lor in logical formulas and \vee in lattice theory for readable source, though both render the same.

Also listed under: Boolean Algebra, Computer Science

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Logical Or: $\lor$

\[ p \lor \neg p \equiv \top \]
\end{document}

Related symbols

• Right Arrow (Double)\Rightarrow
• Logical And\land
• Left Arrow (Double)\Leftarrow
• Negation\neg
• Left Right Arrow (Double)\Leftrightarrow
• Not Exists\nexists

Frequently asked questions

How do I write Logical Or in LaTeX?

Type \lor in math mode, for example $p \lor \neg p \equiv \top$. It works in plain LaTeX without loading any package.

Which package do I need for \lor?

None. \lor is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \lor in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\lor$ in running text. If you only need the glyph in text, paste the Unicode character ∨ instead (with XeLaTeX or LuaLaTeX and a font that has it).