Set Theory Engine

Mathematical Principles & Theorems

Formalizes axiomatic set theory operations on finite sets \(A, B, C \subseteq \mathcal{U}\): (1) Union \(A \cup B = \{x : x \in A \lor x \in B\}\); (2) Intersection \(A \cap B = \{x : x \in A \land x \in B\}\); (3) Relative Complement \(A \setminus B = \{x : x \in A \land x \notin B\}\); (4) Symmetric Difference \(A \Delta B = (A \cup B) \setminus (A \cap B)\); (5) Cartesian Product \(A \times B = \{(a, b) : a \in A, b \in B\}\); (6) Power Set \(\mathcal{P}(A)\) with cardinality \(|\mathcal{P}(A)| = 2^{|A|}\).

Operating Instructions

• Enter comma-separated element sets for Set A, Set B, and Set C in the parameter inputs.
• Select set operation: Union, Intersection, Difference, Symmetric Difference, Cartesian Product, or Power Set.
• Click Evaluate to compute resulting elements, set cardinality, and subset containment relations.
• Inspect the interactive Venn diagram visualization highlighting the selected Boolean region.