Set Theory

$x \in A \subset \Omega$

$A^C = {x \in \Omega, ~ x \notin A }$

$A \cup B = {x \in \Omega, ~ x \in A \vee ~ x \in B}$

$A \cap B = {x \in \Omega, ~ x \in A & ~ x \in B}$

$A \subset B \leftrightarrow \forall x \in A, x \in B$

$A = B \leftrightarrow A \subset B, B \subset A$

$A - B = A \cap B^C$

$A \cap B \subset A \subset A \cup B$