Sets and Combinatorics

Set is a fundamental, abstract notion. A set is defined as a collection of objects, which are called the elements or points of the set. The notions of union ($A \cup B$, where $A$ and $B$ are each sets), intersection ($A \cap B$), and complement ($A^c$) correspond to everyday usage. Thus, if $A = \{ a,b\}$ and $B = \{ b,c\}$, $A \cup B = \{ a,b,c\}$, $A \cap B = \{ b\}$, and $A^c = \{ c,d,\dots ,z\}$ if our world is the English alphabet. Functions can be thought of as operations that map one set onto another.