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.



Recent Updates

  • 08-10-2017 Floyd-Warshall Shortest Paths
  • 08-01-2017 Degree Centrality of a Graph
  • 06-03-2017 Tarjan's Strongly Connected Components Algorithm
  • 03-20-2017 Longest Common Subsequence
  • 10-27-2016 Independent Set Puzzles
  • 06-28-2016 Lets Learn About XOR Encryption
  • 06-15-2016 Discrete-time Markov Chains
  • 03-01-2016 Topological Sort
  • 01-21-2016 The RSA Algorithm
  • 11-20-2015 How To Take Notes in Math Class
  • 10-28-2015 The Depth-First-Search Algorithm
  • 10-28-2015 The Breadth-First-Search Algorithm
  • 09-23-2015 ID3 Algorithm Decision Trees
  • 07-08-2015 Clique Problem Puzzles
  • 06-25-2015 Unidirectional TSP Puzzles
  • 04-04-2015 Learn About Descriptive Statistics
  • 02-19-2015 Slope Formula
  • 01-15-2015 Interactive Midpoint Formula
  • 12-18-2014 Triangle Sum Puzzle
  • 12-02-2014 The Bridge Crossing Problem