$\text{Let}\ C = \{1,2,3,4\},\ D = \{3,4,5\}$
| Symbol | Meaning | Example |
|---|---|---|
| $\{\}$ | Set, Collection of elements | $\{1,2,3,4\}$ |
| $A \cup B$ | Union, in A or B (or both) | $C \cup D = \{1,2,3,4,5\}$ |
| $A \cap B$ | Intersection, in both A and B | $C \cap D = \{3,4\}$ |
| $A \subseteq B$ | Subset, every element of A is in B | $\{3,4,5\} \subseteq D$ |
| $A \subset B$ | Proper Subset, every element of A is in B, but B has more elements | $\{3,5\} \subset D$ |
| $A \not\subset B$ | Not a subset, A is not a subset of B | $\{1,6\} \not\subset C$ |
| $A \supseteq B$ | Superset, A has same elements as B, or more | $\{1,2,3\} \supseteq \{1,2,3\}$ |
| $A \supset B $ | Proper Superset, A has B's elements and more | $\{1,2,3,4\} \supset \{1,2,3\}$ |
| $A \not\supset B$ | Not a Superset, A is not the superset of B | $\{1,2,6\} \not\subset \{1,9\}$ |
| $A^{\complement}$ | Complement, elemets not in A | $D^{\complement} = \{1,2,6,7\}$ $\text{When} \ \mathbb{U} = \{1,2,3,4,5,6,7\}$ |
| $A - B$ | Difference, in A but not in B | $\{1,2,3,4\} - \{3,4\} = \{1,2\}$ |