The brief proof for boolean algebraic structure of multi map symbol system

Boolean algebra is a system suit with which computer can carry on logic operation. It provides theory base and mathematical tool for automatic mapping .In this paper according to the mathematical principle that the power set P(X)of discussion field X belongs Boolean algebra and its partial-ordering relation is contain relation, the authors have given the brief proof which is different from application definition and theorem of Boolean algebra through change discussion field X for the Boolean algebraic construction of map image system, map symbol system and cartographic data base system, and multi map symbol system respectively. By some examples, the authors have explained the Boolean operation in map image system. It concludes that Boolean operation is also suitable in map symbol system and cartographic database system, which with point set as basic element.