# Venn Diagram

A Venn Diagram is a pictorial representation of the relationships between sets.

We can represent sets using Venn diagrams. In a Venn diagram, the sets are represented by shapes; usually circles or ovals. The elements of a set are labeled within the circle.

The following diagrams show the set operations and Venn Diagrams for Complement of a Set, Disjoint Sets, Subsets, Intersection and Union of Sets. Scroll down the page for more examples and solutions.

Set Operations and Venn Diagrams

The set of all elements being considered is called the Universal Set (U) and is represented by a rectangle.

The complement of A, A', is the set of elements in U but not in A. A' ={x| x ∈ U and x ∉ A}

Set A and B are disjoint sets if they do not share any common elements.

B is a proper subset of A. This means B is a subset of A, but B ≠ A.

The intersection of A and B is the set of elements in both set A and set B. A ∩ B = {x| x ∈ A and x ∈ B}

The union of A and B is the set of elements in set A or set B. A ∪ B = {x| x ∈ A or x ∈ B}

A ∩ ∅ = ∅

A ∪ ∅ = A