12.8.5 Set operators

The following operations on sets can be performed with operators: union, difference, symmetric difference, inclusion and intersection. Elements can be added or removed from the set with the Include or Exclude operators. The operators needed for this are listed in table (12.6).


Table 12.6: Set operators

OperatorAction


+ Union
- Difference
* Intersection
>< Symmetric difference
<= Contains
include include an element in the set
exclude exclude an element from the set
in check wether an element is in a set



The set type of the operands must be the same, or an error will be generated by the compiler.

The following program gives some valid examples of set operations:

Type  
  Day = (mon,tue,wed,thu,fri,sat,sun);  
  Days = set of Day;  
 
Procedure PrintDays(W : Days);  
Const  
  DayNames : array [Day] of String[3]  
           = (’mon’,’tue’,’wed’,’thu’,  
              ’fri’,’sat’,’sun’);  
Var  
  D : Day;  
  S : String;  
begin  
  S:=’’;  
  For D:=Mon to Sun do  
    if D in W then  
      begin  
      If (S<>’’) then S:=S+’,’;  
      S:=S+DayNames[D];  
      end;  
  Writeln(’[’,S,’]’);  
end;  
 
Var  
  W : Days;  
 
begin  
   W:=[mon,tue]+[wed,thu,fri]; // equals [mon,tue,wed,thu,fri]  
   PrintDays(W);  
   W:=[mon,tue,wed]-[wed];     // equals [mon,tue]  
   PrintDays(W);  
   W:=[mon,tue,wed]-[wed,thu];     // also equals [mon,tue]  
   PrintDays(W);  
   W:=[mon,tue,wed]*[wed,thu,fri]; // equals [wed]  
   PrintDays(W);  
   W:=[mon,tue,wed]><[wed,thu,fri]; // equals [mon,tue,thu,fri]  
   PrintDays(W);  
end.

As can be seen, the union is equivalent to a binary OR, while the intersection is equivalent to a binary AND, and the summetric difference equals a XOR operation.

The Include and Exclude operations are equivalent to a union or a difference with a set of 1 element. Thus,

  Include(W,wed);

is equivalent to

  W:=W+[wed];

and

  Exclude(W,wed);

is equivalent to

  W:=W-[wed];

The In operation results in a True if the left operand (an element) is included of the right operand (a set), the result will be False otherwise.