**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 $B$. |