Chapter 1: Sets and Set Theory

These flashcards cover key terminology and definitions related to sets and set theory.

Set

A well-defined collection of objects.

Empty Set

A set that does not contain any elements, denoted by φ or { }.

Finite Set

A set that contains a definite number of elements.

Infinite Set

A set that does not have a finite number of elements.

Subset

A set A is a subset of B (A ⊂ B) if every element of A is also an element of B.

Equal Sets

Two sets A and B are equal if they have exactly the same elements, written as A = B.

Union of Sets

The union of sets A and B (A ∪ B) is the set of all elements that are in A, in B, or in both.

Intersection of Sets

The intersection of sets A and B (A ∩ B) is the set of all elements that are common to both A and B.

Difference of Sets

The difference of sets A and B (A - B) is the set of elements that belong to A but not to B.

Complement of a Set

The complement of a set A (denoted A′) is the set of all elements in the universal set U that are not in A.

Power Set

The collection of all subsets of a set A, denoted by P(A).

Venn Diagram

A diagram that represents the relationships between different sets using circles.

De Morgan's Laws

Rules that relate the complement of unions and intersections of sets: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′.

Cardinality

The number of elements in a set, denoted n(S).

Roster Form

A way to represent a set by listing all its elements within braces { }.

Set-builder Form

A way to define a set by specifying a property that its members satisfy.

Natural Numbers (N)

The set of positive integers (1, 2, 3, …).

Integers (Z)

The set of whole numbers that include positive, negative numbers and zero.

Rational Numbers (Q)

The set of numbers that can be expressed as the quotient of two integers, where the denominator is not zero.

Real Numbers (R)

The set of all rational and irrational numbers.