xvi Preliminaries and Notation fred,blue}CS {-23,-345,-9999,-12}CS2 fred,white,black}S fred,yellow}Cfred,yellow} Intersection Set S is the intersection of sets S'and S"if every member of S is a member of S' and also a member of S".This is denoted as:S=S'nS". fred,blue)=fred,yellow,blue,whitenblue,black,red} Union Set S is the union of sets S'and S"if every member of S is either a member of S'or it is a member of S"or it is a member of both S'and S".This is denoted as: S=S'US". fred,blue,white,black}=fred,blue,white}Ufblue,black,red} Set Difference Set S is the set difference of sets S'and S"if every member of S is a member of S'but is not a member of S".This is denoted as:S=S'-S". fred,blue}=fred,yellow,blue,white}-(black,yellow,white} Cartesian product The cartesian product of two sets S and S'is defined as a set of ordered pairs (x,y)(x,y)(y,x))such that x is a member of S and y is a member of S'; that is S*S'={(x,y)lx∈S andy∈S'}. For instance {red,blue}*{4,8}={(red,4),(red,8),(blue,4),(blue,8)} It can be shown that IS S'l =ISIx IS'l for finite sets.Similarly,the cartesian product of n sets S1,S2,...,Sn can be defined as S1 S2 *...Sn={(a1,a2,...,an)l aE S:for every i Each (v1,v2,...,vn)ES*S2 *...*Sn is called an n-ary tuple. Sets of Sets Sets can be members of other sets.For instance,a set of families is a set of sets