Set Operations

Understanding Set Theory is fundamental to understanding advanced mathematics. Iv wrote these scripts so that users could begin to play with the different set operations that are taught in a basic set theory course. Here, the sets are limited to positive integers and we're only looking at a few operations, in particular the union, intersection, difference, symmetric difference, and cross product of two sets. I will explain what each of these is below.

The union of the sets S1 and S2 is the set S1 [union] S2, which contains the elements that are in S1 or S2 (or in both).
Note: S1 [union] S2 is the same as S2 [union] S1.

The intersection of the sets S1 and S2 is the set S1 [intersect] S2, which contains the elements that are in BOTH S1 and S2.
Note: S1 [intersect] S2 is the same as S2 [intersect] S1.

The difference between the sets S1 and S2 is the set S1 / S2, which contains the elements that are in S1 and not in S2.
. Note. S1 / S2 IS NOT the same as S2 / S1.
Note. S1 / S2 is the same as S1 [intersect] [not]S2.

The symmetric difference between the sets S1 and S2 is the set S1 [symm diff] S2, which contains the elements that are in S1 and not in S2, or the elements that are in S2 and not in S1.
Note. S1 [symm diff] S2 is the same as S2 [symm diff] S1.
Note. S1 [symm diff] S2 is the same as (S1 [intersect] [not] S2) [union] (S2 [intersect] [not] S1).

The Cartesian product of the two sets S1 and S2 is the set of all ordered pairs (a, b), where a [in] S1 and b [in] S2.