## Definition ==Set Theory== is the branch of mathematics that studies collections of objects (called sets) and the relationships between them. Sets are described by listing their elements or by specifying a property that all elements share, and they form the foundational language for defining probability spaces, events, and operations on events. > [!example]- Given $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, what are $A \cup B$, $A \cap B$, and $A \setminus B$? > - $A \cup B = \{1, 2, 3, 4, 5, 6\}$ — all elements in either set. > - $A \cap B = \{3, 4\}$ — elements common to both sets. > - $A \setminus B = \{1, 2\}$ — elements in $A$ but not in $B$.