Set Symbols
| Symbol | Meaning | Example |
|---|---|---|
| $\{\,...\,\}$ | Set | $A = \{3,7,9\}$ $B = \{2,3,9\}$ |
| $\emptyset$ | empty Set | $\emptyset = \{\,\}$ |
| $\{x\, \vert \cdots\}$ | Set of all $x$ with ... | $\{x\,\vert\,x$ is a prime number$\}$ |
| $\in$ | (is) element of | $7 \in A$ |
| $\notin$ | (is) not element of | $7 \notin B$ |
| $\cap$ | Intersection; in $A$ and in $B$ | $A \cap B = \{3,9\}$ |
| $\cup$ | Union; in $A$ or in $B$ | $A \cup B = \{2,3,7,9\}$ |
| \ | Difference; in $A$ and not in $B$ | $A \setminus B = \{7\}$ |
| $\subset$ | (is) subset of | $A \subset (A \cup B)$ |
| $\not\subset$ | (is) not subset of | $A \not\subset (A \cap B)$ |
| $\supset$ | (is) superset of | $(A \cup B) \supset A$ |
| $\not\supset$ | (is) not superset of | $(A \cap B) \not\supset A$ |
Logic Symbols
| Symbol | Meaning | Example |
|---|---|---|
| $\land$ | and | $A \cap B :=$ $\{x\,\vert\,x \in A \,\land\, x \in B\}$ |
| $\lor$ | or | $A \cup B :=$ $\{x\,\vert\,x \in A \,\lor\, x \in B\}$ |
| $\veebar$ | exclusive or | $A \triangle B :=$ $\{x\,\vert\,x \in A \,\veebar\, x \in B\}$ |
| $\lnot$ | not | $\lnot(x \in A) \iff x \notin A$ |
| $\Longrightarrow$ | if ... then | $x \in A \cap B \Longrightarrow x \in A$ |
| $\forall$ | for all; every | $\forall x \in A : x \in A \cup B$ |
| $\exist$ | there exists; for some | $\exists x \in A : x \in A \cap B$ |
| $\exist!$ | there exists exactly one | $\exists! x \in A : x \in A \setminus B$ |
| $\nexists$ | there exists no; for no | $\nexists x \in A : x \in B \setminus A$ |