Set

A set is a collection in which:

  • Each item is distinct. There are no duplicates
  • There’s no sense of order. You cannot sort a set.
OperationSyntaxExample
Union\(A \cup B\)\(\{1, 2, 3\} \cup \{2, 3, 4\} = \{1, 2, 3, 4\}\)
Intersection\(A \cap B\)\(\{1, 2, 3\} \cap \{2, 3, 4\} = \{2, 3\}\)
Set difference\(A - B\)\(\{1, 2, 3\} - \{2, 3, 4\} = \{1, 2\}\)
Symmetric difference\(A \triangle B\)\(\{1, 2, 3\} \triangle \{2, 3, 4\} = \{1, 4\}\)

Union \(A \cup B\)

  • Copy set \(A\) into set \(X\)
  • Add all values of set \(B\) into set \(X\), skipping duplicates

Intersection \(A \cap B\)

  • New empty set \(X\)

  • Foreach value in \(A\)

    • If it’s not in \(B\), then add to \(X\)

  • Foreach value in \(B\)

    • If it’s not in \(A\), then add to \(X\)

Set difference \(A - B\)

  • Copy set \(A\) into set \(X\)
  • Remove all values of set \(B\) from set \(X\), skipping values that don’t exist.

Symmetric difference \(A \triangle B\)

Can be calculated using the previous operations:

$$ A \triangle B = (A \cup B) - (A \cap B) $$

For example:

$$ \begin{align} \{1,2,3\} \triangle \{2,3,4\} &= (\{1,2,3\} \cup \{2,3,4\}) - (\{1,2,3\} \cap \{2,3,4\}) \\ &= \{1,2,3,4\} - \{2,3\} \\ &= \{1,4\} \end{align} $$

Naming differences in .NET

Math.NET HashSet<T>
Union.UnionWith(IEnumerable<T>)
Intersection.IntersectWith(IEnumerable<T>)
Set difference.Except(IEnumerable<T>)
Symmetric difference.SymmetricExceptWith(IEnumerable<T>)

Reference

May 5, 2021