Intersection in LaTeX (\cap)

Where it is used

Forms the intersection of sets: the elements common to all of them.

\cap is a binary operator written between sets, as in A \cap B, while \bigcap is the large-operator version for families, \bigcap_{n} U_n. In probability it represents joint events, so P(A \cap B) = P(A)P(B) defines independence. Its logical counterpart is \land (and), and the lattice-theory meet \wedge looks similar but is a different glyph. De Morgan laws pair it with union: (A \cup B)^c = A^c \cap B^c. If A \cap B = \emptyset, the sets are disjoint.

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}
Intersection: $\cap$

\[ (A \cup B)^c = A^c \cap B^c \]
\end{document}

Related symbols

• Empty Set\emptyset
• Union\cup
• Partial Derivative\partial
• Subset\subset
• Nabla\nabla
• Not Element Of\notin

Frequently asked questions

How do I write Intersection in LaTeX?

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

Which package do I need for \cap?

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

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

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