Definitions of Set Notation

Basic set notation. Let $A$ and $B$ be sets.

$x\in A$ means	$x$ is an element of $A$
$x\notin A$ means	$x$ is not an element of $A$
$\{x\ \|\ P(x) \}=$	the set of all elements $x$ such that $P(x)$ is true

(The above notation is called set-builder notation. $P(x)$ is any property that is either true or false, depending on $x$.)

$A=B$ is true when	$A$ and $B$ have the same elements
$A \cup B=$	$\{x \ \|\ x \in A \mbox{or} x \in B \mbox{ (or both)}\}$ $=$ the union of $A$ and $B$.
$A \cap B=$	$\{x \ \|\ x \in A \mbox{and} x \in B\}$ $=$ the intersection of $A$ and $B$.