set theory

notation

$x \in A$

$x$ is an element of set $A$

$A \subset B$

$A$ is a subset of $B$ . All elements in $A$ are also in $B$ . There are elements in $B$ that are not in $A$ .

$A \subseteq B$

$A$ is a subset of $B$ . All elements in $A$ are also in $B$ . There could be elements in $B$ that are not in $A$ or they could be equal.

$A \cup B$

Union of $A$ and $B$ .

$A \cap B$

Intersection of $A$ and $B$ .

$A \backslash B$

set difference of $A$ and $B$ . $\{x : x \in A , x \notin B\}$ .