Set Operations#

All set operations output a set of unique values unless the keyword ALL is appended after.

UNION#

\[ A \cup B\]

  • Distinct $\( |A| + |B|\)$

  • ALL $\( |A| + |B|\)$

INTERSECT#

\[ A \cap B\]

  • Distinct $\( \min(|A|, |B|)\)$

  • ALL $\( \sum_i\min(|a_i|,|b_i|), \qquad a \subseteq A,~ b \subseteq B\)$

EXCEPT#

\[ A \backslash B\]

  • ALL $\( \sum_i \Delta_i, \qquad a \subseteq A,~ b \subseteq B\\ \Delta_i = \begin{cases} 0~, &|a_i| - |b_i| < 0 \\ |a_i| - |b_i|~, &\text{else}\\ \end{cases} \)$