3 Set operations

• $X = S \cup T$ is the union of $S$ and $T$ . This means that $\forall e: (e \in X) \leftrightarrow ((e \in S) \vee (e \in T))$ . This means that an element is in $X$ if and only if it is in $S$ or it is in $T$ .
• $X = S \cap T$ is the intersection of $S$ and $T$ . This means that $\forall e: (e \in X) \leftrightarrow ((e \in S) \wedge (e \in T))$ . In English: an element is in $X$ if and only if it is in $S$ and also in $T$ .
• $X = S + e$ ($e$ is an element) is the same as $X = S \cup \{e\}$ .
• $X = S \setminus T$ is the difference of $S$ and $T$ . This means that $\forall e \in X: (e \in S) \wedge \neg(e \in T)$ . In English, all elements in $X$ are unique to $S$ .
• $X = S - e$ ($e$ is an element) is the same as $X = S \setminus \{e\}$