Set Theory Notation.

\(\{, \}\)

We use these braces to enclose the elements of a set. So \(\{1,2,3\}\) is the set containing 1, 2, and 3.

\(\st\)

\(\{x \st x > 2\}\) is the set of all \(x\) such that \(x\) is greater than 2.

\(\in\)

\(2 \in \{1,2,3\}\) asserts that 2 is an element of the set \(\{1,2,3\}\text{.}\)

\(\not\in\)

\(4 \notin \{1,2,3\}\) because 4 is not an element of the set \(\{1,2,3\}\text{.}\)

\(\subseteq\)

\(A \subseteq B\) asserts that \(A\) is a subset of \(B\): every element of \(A\) is also an element of \(B\text{.}\)

\(\subset\)

\(A \subset B\) asserts that \(A\) is a proper subset of \(B\): every element of \(A\) is also an element of \(B\text{,}\) but \(A \ne B\text{.}\)

\(\cap\)

\(A \cap B\) is the intersection of \(A\) and \(B\): the set containing all elements which are elements of both \(A\) and \(B\text{.}\)

\(\cup\)

\(A \cup B\) is the union of \(A\) and \(B\): is the set containing all elements which are elements of \(A\) or \(B\) or both.

\(\times\)

\(A \times B\) is the Cartesian product of \(A\) and \(B\): the set of all ordered pairs \((a,b)\) with \(a \in A\) and \(b \in B\text{.}\)

\(\setminus\)

\(A \setminus B\) is set difference between \(A\) and \(B\): the set containing all elements of \(A\) which are not elements of \(B\text{.}\)

\(\bar{A}\)

The complement of \(A\) is the set of everything which is not an element of \(A\text{.}\)

\(\card{A}\)

The cardinality (or size) of \(A\) is the number of elements in \(A\text{.}\)