##Let $A$ and $B$ be sets. #$x\in A$ $\Leftrightarrow$ $x$ is an element of $A$ #$\{x\in A\ |\ P(x)\}$ $=$ the set of all $x\in A$ such that $P(x)$ is true #$y\in\{x\in A\ |\ P(x)\}$ $\Leftrightarrow$ $y\in A$ and $P(y)$ is true #$A=B$ $\Leftrightarrow$ $\forall x(x \in A \leftrightarrow x \in B)$ <br> #$A \subseteq B$ $\Leftrightarrow$ $\forall x(x \in A \to x \in B)$ <br> #$A \cup B$ $=$ $\{x \ |\ x \in A \vee x \in B\}$ <br> #$x\in A \cup B$ $\Leftrightarrow$ $x \in A \vee x \in B$ <br> #$A \cap B$ $=$ $\{x \ |\ x \in A \wedge x \in B\}$ <br> #$x\in A \cap B$ $\Leftrightarrow$ $x \in A \wedge x \in B$ <br> #$A$ and $B$ are disjoint $\Leftrightarrow$ $A \cap B=\emptyset$ <br> #$A - B$ $=$ $\{x \ |\ x \in A \wedge x \notin B\}$ <br> #$x\in A - B$ $\Leftrightarrow$ $x \in A \wedge x \notin B$ <br> #$-B$ $=$ $\{x\ |\ x \notin B\}$<br> #$x\in -B$ $\Leftrightarrow$ $x \notin B$<br>