Subset (⊂ / ⊆) in LaTeX
\subseteq (and the strict form \subset) typeset the subset relation: means every element of A is also an element of B.
LaTeX command
\subseteqNot the symbol you meant? Draw it to find the command →
A subset relation compares two sets rather than an element and a set. says every member of A also belongs to B, and it allows A to equal B. The strict version (or ) additionally requires A and B to be different, so A is a proper subset.
Notation conventions vary by textbook. Many modern texts, especially in analysis, use \subset to mean 'subset, possibly equal', matching what \subseteq means elsewhere. If there is any risk of ambiguity, use \subseteq for the inclusive relation and \subsetneq for the strict one, and say so once at the start of your document.
The superset relations \supseteq and \supset mirror subset in the other direction: says exactly the same thing as . Pairing \subseteq with \supseteq keeps a chain of inclusions readable when the sets get large, for instance \mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}.
Other forms
\subsetsubset (⊂)\supseteqsuperset (⊇)\supsetsuperset (⊃)Examples
$\mathbb{N} \subseteq \mathbb{Z}$the naturals sit inside the integers
$A \subsetneq B$A is a proper (strict) subset of B
$\{1,2\} \subset \{1,2,3\}$a strict subset using \subset
$B \supseteq A$the same relation written as a superset
$\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}$a chain of standard number-set inclusions
Tips and common mistakes
- Decide early whether
\subsetmeans 'subset' or 'proper subset' in your document, then stay consistent; conventions differ between authors. - Use
\subseteqwhen you want to explicitly allow equality, and\subsetneq(from amssymb, built in on KaTeX) when you want to explicitly exclude it. - Do not use
\subsetwhere you mean\in; a single element like 2 is a member of\mathbb{N}, not a subset of it (\{2\} is the subset). \supseteqand\supsetare just\subseteqand\subsetwith the operands swapped; pick whichever reads better in the sentence.- For 'is not a subset of', use
\nsubseteqrather than manually crossing out the symbol.
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What is the difference between \subset and \subseteq?
In the strict amsmath convention, \subseteq allows the two sets to be equal, while \subset (used as 'proper subset') requires them to differ. Many authors instead use \subset loosely to mean \subseteq, so check the convention in whatever text you are following, or state your own at the outset.
How do I show a proper (strict) subset in LaTeX?
Use \subsetneq (or \varsubsetneq for a variant glyph), which unambiguously means 'subset but not equal'.
What is the symbol for superset?
\supseteq for 'superset or equal' and \supset (or \supsetneq for strict) for superset, the mirror images of the subset symbols.
How do I write 'is not a subset of'?
Use \nsubseteq, which renders the subset symbol with a slash through it.