Sets and Set Theory Concepts

These flashcards cover vocabulary related to sets and set theory, including definitions and important concepts.

Set

A structure representing an unordered collection of zero or more distinct objects.

Set Equality

Two sets are equal if they contain exactly the same elements.

Set Builder Notation

A notation to define a set by a property, for example, {x | P(x)}.

Infinite Sets

Sets that are not finite and do not have an end.

Member of a Set

The proposition that an object x is an element of set S, denoted as x Î S.

Empty Set

The unique set containing no elements, denoted as Ø or {}.

Subset

Set S is a subset of set T if every element of S is also in T, denoted S Í T.

Superset

Set S is a superset of set T if T is a subset of S, denoted S Ê T.

Cardinality

The measure of the number of distinct elements in a set, denoted |S|.

Power Set

The set of all subsets of a set S, denoted P(S).

Cartesian Product

For sets A and B, the Cartesian product A×B is the set of all ordered pairs (a, b) where a Î A and b Î B.

Union of Sets

The set containing all elements from both sets A and B, denoted A È B.

Intersection of Sets

The set containing elements that are in both sets A and B, denoted A Ç B.

Disjoint Sets

Two sets are disjoint if their intersection is empty, meaning they share no elements.

Set Difference

The difference between sets A and B, denoted A - B, is the set of elements in A that are not in B.

Complement of a Set

The complement of set A with respect to the universe U, denoted A', is U - A.

Symmetric Difference

The set of elements that are in exactly one of the two sets A and B, denoted A Δ B.

DeMorgan's Law

A law relating the union and intersection of sets: A È B = (A' ∩ B').

Inclusion-Exclusion Principle

A formula to find the number of elements in the union of two sets: |A È B| = |A| + |B| - |A Ç B|.