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[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]