Subset or Equal in LaTeX (\subseteq)

Where it is used

States that every element of the left set also belongs to the right set; the sets may be equal.

Use \subseteq for the inclusion that allows equality, as in A \subseteq A, and in definitions like a topology being closed under unions of subfamilies \mathcal{U} \subseteq \tau. Many authors use plain \subset with the same meaning, while others reserve \subset for proper inclusion, so it is worth stating your convention. For proper inclusion unambiguously, use \subsetneq. The negation is \nsubseteq or \not\subseteq. To show two sets are equal, a standard proof shows A \subseteq B and B \subseteq A.

Also listed under: Set Theory

Minimal compilable example

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

\documentclass{article}
\begin{document}
Subset or Equal: $\subseteq$

\[ A \subseteq B \land B \subseteq A \iff A = B \]
\end{document}

Related symbols

• Proper Subset\subsetneq
• Subset\subset
• Superset\supset
• Congruent\cong
• Superset or Equal\supseteq
• Similar To\sim

Frequently asked questions

How do I write Subset or Equal in LaTeX?

Type \subseteq in math mode, for example $A \subseteq B \land B \subseteq A \iff A = B$. It works in plain LaTeX without loading any package.

Which package do I need for \subseteq?

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

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

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