Set Theory
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$x \in A \subset \Omega$
$A^C = {x \in \Omega, ~ x \notin A }$
$A \cup B = {x \in \Omega, ~ x \in A \vee ~ x \in B}$
$A \cap B = {x \in \Omega, ~ x \in A & ~ x \in B}$
$A \subset B \leftrightarrow \forall x \in A, x \in B$
$A = B \leftrightarrow A \subset B, B \subset A$
$A - B = A \cap B^C$
$A \cap B \subset A \subset A \cup B$