Venn Diagram Calculator

Calculate unions, intersections, and probabilities for Venn diagrams. Effortlessly visualize complex data intersections and set relationships with our intuitive calculator.

Elements only in Set A

Elements only in Set B

Elements in both A and B

Elements outside both sets (in universal set)

Union: A∪B = (Only A) + (A∩B) + (Only B). Intersection: A∩B = elements in both. P(A∪B) = P(A) + P(B) - P(A∩B)
Set A=15, Set B=20, Both=10, Neither=5: Total A=25, Total B=30, Union=45, Universal=50. P(A)=50%, P(B)=60%, P(A∩B)=20%

What is a Venn diagram and what does it show?

A Venn diagram uses overlapping circles to visualize relationships between sets. Each circle represents a set, overlapping regions show elements in common (intersection), and non-overlapping parts show unique elements. It helps visualize unions, intersections, and complements of sets.

What is the difference between union and intersection?

Union (A ∪ B) = all elements in A OR B or both (combine sets, count each element once). Intersection (A ∩ B) = elements in BOTH A AND B (overlap only). Example: A={1,2,3}, B={2,3,4}. A∪B={1,2,3,4}, A∩B={2,3}.

How do I calculate probabilities from a Venn diagram?

Divide each region by the universal set total. P(A) = (Only A + Both) / Total. P(A∩B) = Both / Total. P(A∪B) = (Only A + Both + Only B) / Total. These satisfy: P(A∪B) = P(A) + P(B) - P(A∩B).

What are disjoint or mutually exclusive sets?

Disjoint sets have NO elements in common (intersection is empty). In Venn diagrams, circles don't overlap. Example: Even numbers and odd numbers are disjoint. For disjoint sets: A∩B = ∅ (empty), P(A∪B) = P(A) + P(B).

How do I use Venn diagrams to solve word problems?

Steps: (1) Identify the sets (e.g., students taking Math, students taking Science), (2) Find intersection (both), (3) Calculate "only" regions by subtracting intersection from totals, (4) Add all regions for union, (5) Subtract from universal set for "neither". Label diagram clearly!