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 \(A \cup B\)

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

Intersection \(A \cap B\)

  1. New empty set \(X\)

  2. Foreach value in \(A\)

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

  3. Foreach value in \(B\)

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

Set difference \(A - B\)

  1. Copy set \(A\) into set \(X\)
  2. 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

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