Sets

A set is a collection of elements of same type. Pascal allows defining the set data type. The elements in a set are called its members. In mathematics, sets are represented by enclosing the members within braces{}. However, in Pascal, set elements are enclosed within square brackets [], which are referred as set constructor.

Defining Set Types and Variables

Pascal Set types are defined as

type
set-identifier = set of base type;

Variables of set type are defined as

var
s1, s2, ...: set-identifier;

or,

s1, s2...: set of base type;

Examples of some valid set type declaration are −

type
Days = (mon, tue, wed, thu, fri, sat, sun);
Letters = set of char;
DaySet = set of days;
Alphabets = set of 'A' .. 'Z';
studentAge = set of 13..20;

Set Operators

You can perform the following set operations on Pascal sets.

Sr.No	Operations & Descriptions
1	UnionThis joins two sets and gives a new set with members from both sets.
2	DifferenceGets the difference of two sets and gives a new set with elements not common to either set.
3	IntersectionGets the intersection of two sets and gives a new set with elements common to both sets.
4	InclusionA set P is included in set Q, if all items in P are also in Q but not vice versa.
5	Symmetric differenceGets the symmetric difference of two sets and gives a set of elements, which are in either of the sets and not in their intersection.
6	InIt checks membership.

Following table shows all the set operators supported by Free Pascal. Assume that S1 and S2 are two character sets, such that −

S1 := ['a', 'b', 'c'];

S2 := ['c', 'd', 'e'];

Operator	Description	Example
+	Union of two sets	S1 + S2 will give a set[‘a’, ‘b’, ‘c’, ‘d’, ‘e’]
–	Difference of two sets	S1 – S2 will give a set[‘a’, ‘b’]
*	Intersection of two sets	S1 * S2 will give a set[‘c’]
><	Symmetric difference of two sets	S1 >< S2 will give a set [‘a’, ‘b’, ‘d’, ‘e’]
=	Checks equality of two sets	S1 = S2 will give the boolean value False
<>	Checks non-equality of two sets	S1 <> S2 will give the boolean value True
<=	Contains (Checks if one set is a subset of the other)	S1 <= S2 will give the boolean value False
Include	Includes an element in the set; basically it is the Union of a set and an element of same base type	Include (S1, [‘d’]) will give a set[‘a’, ‘b’, ‘c’, ‘d’]
Exclude	Excludes an element from a set; basically it is the Difference of a set and an element of same base type	Exclude (S2, [‘d’]) will give a set[‘c’, ‘e’]
In	Checks set membership of an element in a set	[‘e’] in S2 gives the boolean value True

Example

The following example illustrates the use of some of these operators −

Live Demo

program setColors;
type  
color = (red, blue, yellow, green, white, black, orange);  
colors = set of color;  
 
procedure displayColors(c : colors);  
const  
names : array [color] of String[7]  
  = ('red', 'blue', 'yellow', 'green', 'white', 'black', 'orange');  
var  
   cl : color;  
   s : String;  

begin  
   s:= ' ';  
   for cl:=red to orange do  
      if cl in c then  
      begin  
         if (s<>' ') then s :=s +' , ';  
         s:=s+names[cl];  
      end;  
   writeln('[',s,']');  
end;  
 
var  
   c : colors;  
 
begin  
   c:= [red, blue, yellow, green, white, black, orange];
   displayColors(c);

   c:=[red, blue]+[yellow, green]; 
   displayColors(c);  

   c:=[red, blue, yellow, green, white, black, orange] - [green, white];     
   displayColors(c);    

   c:= [red, blue, yellow, green, white, black, orange]*[green, white];     
   displayColors(c);  

   c:= [red, blue, yellow, green]><[yellow, green, white, black]; 
   displayColors(c);  
end.

When the above code is compiled and executed, it produces the following result −

[ red , blue , yellow , green , white , black , orange]
[ red , blue , yellow , green]
[ red , blue , yellow , black , orange]
[ green , white]
[ red , blue , white , black]