# Pascal - 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

Union

This joins two sets and gives a new set with members from both sets.

2

Difference

Gets the difference of two sets and gives a new set with elements not common to either set.

3

Intersection

Gets the intersection of two sets and gives a new set with elements common to both sets.

4

Inclusion

A set P is included in set Q, if all items in P are also in Q but not vice versa.

5

Symmetric difference

Gets 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

In

It 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 −

```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
= ('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]
```