Mathematical Principles & Theorems
Visualizes set algebra on 2-set and 3-set universes \(\mathcal{U}\). Partitions the universal set into \(2^n\) mutually disjoint Boolean minterm regions. Principle of Inclusion-Exclusion for 3 sets: \(|A \cup B \cup C| = |A| + |B| + |C| - (|A \cap B| + |B \cap C| + |A \cap C|) + |A \cap B \cap C|\). De Morgan's laws and set identities visually verified by region shading.
Operating Instructions
- Select 2-Set or 3-Set Venn diagram layout.
- Enter element lists or cardinalities for sets A, B, and C.
- Click individual Venn diagram sectors to highlight and compute complex Boolean set expressions (e.g., \((A \cap B) \setminus C\)).
- Review the calculated region cardinalities and inclusion-exclusion arithmetic summaries.