Thispaperdiscussesthedefinitionsandpropertiesoftwokindsoffundamentalsymmetricfunctions,whicharebasedonAND-OR-NOTalgebraicsystemandAND-ExclusiveORalgebraicsystem,respectively.Baseduponit,somemappingtransformationmethodsbetweentwokindsofexpansioncoefficientsofanarbitrarysymmetric,functioninthecompletesetoftwofundamentalsymmetricfunctions.