Venn Diagrams and Set Theory Vocabulary

Key vocabulary terms from the lecture notes on Venn diagrams, universal sets, and set operations (intersections, unions, complements, subsets, and disjoint sets).

Venn diagram

A diagram that visually represents relationships between sets, typically with circles inside a rectangle representing the universal set; used to illustrate union, intersection, and complement.

Universal set

The container for all elements under discussion; in the notes, the universal set is all numbers from one to twenty (less than 20).

Set

A collection of distinct objects considered as a single entity in set theory.

Element

An individual object that belongs to a set.

Intersection

The elements that are in both sets A and B; denoted A ∩ B.

Union

The elements that are in A or B or both; denoted A ∪ B.

Complement

The elements in the universal set that are not in a given set; denoted A′ (A prime).

Subset

A set A is a subset of B if every element of A is also an element of B; denoted A ⊆ B.

Disjoint sets

Two sets that have no elements in common; their circles in a Venn diagram do not overlap.

Overlap

The region where two sets intersect in a Venn diagram; represents elements common to both sets.

A ∩ B (Intersection notation)

The notation for the intersection of sets A and B; the elements common to both.

A ∪ B (Union notation)

The notation for the union of sets A and B; the elements in A or B or both.