Union in LaTeX (\cup)

Where it is used

Forms the union of sets: all elements that belong to at least one of them.

\cup is a binary operator, as in A \cup B, and gets medium spacing on both sides. For a union over an indexed family, use the large operator \bigcup, which stacks limits in display mode: \bigcup_{i=1}^{\infty} A_i. The disjoint union is often written \sqcup or \dot\cup. In probability, A \cup B corresponds to the event "A or B", giving P(A \cup B) = P(A) + P(B) - P(A \cap B). Do not use the letter U or the logical \lor in place of set union.

Also listed under: Advanced Operators, Set Theory

Minimal compilable example

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

\documentclass{article}
\begin{document}
Union: $\cup$

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\end{document}

Related symbols

• Intersection\cap
• Subset\subset
• Empty Set\emptyset
• Not Element Of\notin
• Partial Derivative\partial
• Element Of\in

Frequently asked questions

How do I write Union in LaTeX?

Type \cup in math mode, for example $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. It works in plain LaTeX without loading any package.

Which package do I need for \cup?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\cup$ 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).