Venn Diagrams and Partitions (Section 1.2)

Vocabulary flashcards covering key terms from the lecture notes on Venn diagrams, universal sets, set operations, cardinality, Cartesian products, and partitions.

Universal set (U)

The set that contains all objects under consideration in a given context.

Subset

A is a subset of U if every element of A is also an element of U.

Complement

Elements of the universal set U not in A.

Intersection

Elements that are in both A and B.

Cardinality (n(S))

The number of elements in a set S.

n(S)

Size or cardinality of set S.

Disjoint sets

Two sets with no elements in common (A ∩ B = ∅).

Pairwise disjoint

A collection of sets where every pair is disjoint.

Partition

A partition of X is a collection of nonempty, pairwise disjoint subsets whose union is X.

Partition principle

If X is partitioned into x1, x2, …, xk, then n(X) = n(x1) + n(x2) + … + n(xk).

Cross product (Cartesian product)

For sets A and B, A × B is the set of all ordered pairs (a,b) with a ∈ A and b ∈ B.

Cardinality of a Cartesian product (n(A × B))

|A × B| = |A| × |B|; the size equals the product of the sizes.

Three-set Venn diagram

A Venn diagram that can represent relationships among up to three sets.