A map, or mapping, is a rule, often expressed as an equation, that specifies a particular element of one set for each element of another set. To help understand the notion of map, it is useful to picture the two sets schematically, and map one onto the other, by drawing connecting arrows from members of the first set to the appropriate members of the second set. For instance, let the set mapped from be well-known cities in Texas, specifically, let A = {Abilene, Amarillo, Dallas, Del Rio, El Paso, Houston, Lubbock, Pecos, San Antonio}. We will map this onto the set containing whole numbers of miles. The rule is that each city maps onto its distance from Abilene. The map can be shown as a diagram in which an arrow points from each city to the appropriate distance.

A relation is a set of ordered pairs for which the...