Lecture Notes: Attendance Procedures and Venn Diagram / Set Theory Concepts

A set of vocabulary-focused flashcards covering attendance procedures from the course page to mark presence, and core set theory concepts illustrated by three-set Venn diagrams, including unions, intersections, inclusion-exclusion, and related example problems.

Attendance

The record of students’ presence in a class; on the course page, submit attendance for today and mark Present, then Save.

No-shows

Students who miss attendance; a set number of no-shows may be reported to the department.

Present

Status indicating a student attended the class session.

Course page (attendance)

The online area of the course site where attendance is managed and submitted.

Submit attendance

The action of recording attendance for a given date on the course page.

Three-set Venn diagram

A diagram with three overlapping circles representing three sets, used to visualize unions, intersections, and complements, with a universal set surrounding them.

Universe (universal set)

The set that contains all elements under consideration in a given problem.

Set

A collection of distinct objects treated as a single group.

Intersection

The elements common to two or more sets (A ∩ B, etc.).

Union

The set of elements that are in at least one of the sets (A ∪ B ∪ C).

Cardinality

The number of elements in a set, denoted |A|.

Inclusion-Exclusion Principle

For three sets A, B, C: |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.

Only region

The part of a Venn diagram that belongs exclusively to one set (not overlapping with others).

All three intersection

The region where all three sets overlap: A ∩ B ∩ C.

Pairwise intersection

The overlaps of two sets at a time (A ∩ B, A ∩ C, B ∩ C), which may include the triple intersection depending on context.

Formats example (library)

A three-set Venn problem with paper, ebooks, and audiobooks illustrating how to use overlaps and the center value to compute counts like ‘only’ and ‘two-format’ overlaps.

All three formats center

The count of patrons who borrow all three formats, located in the center of the Venn diagram.

Paper and Audio only

The two-format overlap for Paper ∩ Audio excluding Ebook (the number who borrow exactly Paper and Audio, not the third format).

Paper total

The total number of patrons who borrow paper, including overlaps with ebooks or audiobooks.

Ebooks total

The total number of patrons who borrow ebooks, including overlaps with paper or audiobooks.

Audiobooks total

The total number of patrons who borrow audiobooks, including overlaps with paper or ebooks.

Dog–Cat–Bird problem

A three-pet Venn problem where x represents the number who own all three pets; used to apply inclusion-exclusion to find all overlapping regions.

All three pets (intersection)

The region where dog, cat, and bird all overlap: Dog ∩ Cat ∩ Bird; the value is often denoted by x in worked problems.