Set Symbols

Written by Jerry Ratzlaff on . Posted in Nomenclature & Symbols for Engineering, Mathematics, and Science

This is a list of the most common set symbols:

 

SymbolDefinitionExample
\(\{ \; \}\) set, a collection \(A= \{ 1, 2, 3, 4 \}\) ,  \(B= \{ 3, 4, 5, 6 \} \)
\(\varnothing\) empty set \(A=\{ \varnothing\} \)
\(\cap\) intersection, belonging to set A or B \(A\cap B =\{3, 4\}\)
\(\cup\) union, belonging to set A or B \(A\cup B =\{1, 2, 3, 4, 5, 6\}\)
     
\(\subset\) strict subset, A is subset of B \(\{3, 4\} \subset \{3, 4, 5, 6\}\)
\(\subseteq\) subset, A subset of B, A included in B \(\{3, 4\} \subseteq \{3, 4\}\)
\(\nsubseteq\) not subset, A not subset of B \(\{6, 7\} \nsubseteq \{3, 4, 5, 6\}\)
     
 \(\supset\) strict superset, A superset of B, B not equal to A \(\{3, 4, 5, 6\} \supset \{3, 4\}\)
 \(\supseteq\) superset, A subset of B, A includes B \(\{3, 4, 5, 6\} \supseteq \{3, 4, 5, 6\}\)
\(\nsupseteq\) not superset, A not superset of B \(\{3, 4, 5, 6\} \nsupseteq \{6, 7\}\)
     
\(\in\) belongs to \(B=\{3, 4, 5, 6\}\) ,  \(3\in B\)
\(\notin\) does not belong to \(B=\{3, 4, 5, 6\}\) ,  \(1\notin B\)
     
= equality, both sets the same A=B \(\{3, 4, 5, 6\} = \{3, 4, 5, 6\}\)
\(-\) relative complement, belongs to B but not A \(A-B = \{5, 6\}\)
\(\ominus\) symmetric difference, belongs to A or B gut no matches \(A \ominus B = \{1, 2, 5, 6\}\)
\(|\;|\) cardinality, element of set B  \(|B|=\{3\}\)