Introduction to Set Theory and Set Operations
Set theory is the branch of mathematical logic that studies sets, which are collections of distinct objects called elements. Formalized by Georg Cantor in the late 19th century, set theory forms the foundational language of modern mathematics, computer science, database queries (SQL joins), and probability.
Sets are typically represented using braces containing comma-separated elements (e.g., A = {1, 2, 3}). When comparing two sets, several operations create new sets based on the relations of their elements: union (combining all elements), intersection (finding shared elements), difference (finding elements in one set but not another), and symmetric difference (finding elements in either set but not both).
This calculator computes all four of these two-set operations. Enter two comma-separated lists of elements, and it computes the union, intersection, both one-way differences, and the symmetric difference, lists each region's cardinality, and displays the overlap on a Venn diagram.