Venn Calculator

Drag and drop elements into sets to see their relationships.

Venn Diagram & Boolean Regions Handbook

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.

Element Pool

Define Sets

Universal Set U

Set A

Set B

Calculated Results

All Sets Summary

Union of All Entered Sets:

Intersection of All Entered Sets:

Complement of Union relative to U:

Circles represent Sets A, B, and C. The rectangle is U.
Visualization is limited to the first three sets.