Set Theory Calculator & Venn Diagram Solver | Union, Intersection, Difference

SET THEORY CALCULATOR & VENN SOLVER

Union · Intersection · Relative Complement · Visualizer

Set Theory

Enter elements for Set A and Set B separated by commas or spaces. The solver will automatically evaluate basic set operations and compute element distributions.

Set A Elements: Comma or space-separated elements

Set B Elements: Comma or space-separated elements

Universal Set U (Optional): Leave blank to default to A ∪ B

Calculated Set Operations

Cardinality |A| 0

Cardinality |B| 0

Union |A ∪ B| 0

Intersection |A ∩ B| 0

Union: $A \cup B$ { }

Intersection: $A \cap B$ { }

Difference: $A \setminus B$ { }

Difference: $B \setminus A$ { }

Symmetric Diff: $A \Delta B$ { }

Complement: $A^c$ ($U \setminus A$) { }

Interactive Venn Diagram Layout

Set Theory & Venn Diagram Analysis

Set Theory provides the foundational framework for modern mathematics, establishing rules for collecting, grouping, and comparing distinct objects. Set operations enable rigorous categorization and evaluation of relationships across data subsets.

1. Fundamental Set Operations

Operation	Symbol / Notation	Formal Definition	Description
Union	$$A \cup B$$	$$\{x \mid x \in A \lor x \in B\}$$	Combines all unique elements present in either Set A, Set B, or both.
Intersection	$$A \cap B$$	$$\{x \mid x \in A \land x \in B\}$$	Contains only elements present simultaneously in both Set A and Set B.
Relative Complement (Diff)	$$A \setminus B$$	$$\{x \mid x \in A \land x \notin B\}$$	Contains elements belonging to Set A that do not exist in Set B.
Symmetric Difference	$$A \Delta B$$	$$(A \setminus B) \cup (B \setminus A)$$	Contains elements belonging to either A or B, but not both.
Absolute Complement	$$A^c \text{ or } A'$$	$$\{x \in U \mid x \notin A\}$$	Contains all elements within Universal Set $U$ that are not in Set A.

2. Key Set Identities

• De Morgan's Laws: $(A \cup B)^c = A^c \cap B^c$ and $(A \cap B)^c = A^c \cup B^c$
• Principle of Inclusion-Exclusion: $|A \cup B| = |A| + |B| - |A \cap B|$

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