Lecture 6 - Set Theory

Vocabulary flashcards for Set Theory based on ITSC 2175 lecture notes.

Set

An unordered collection of distinct objects.

Set Notation

Curly braces {} with commas between elements, e.g., S = {a, b, c, d}.

Element of a Set

An object that belongs to a set (denoted by Î).

Order among elements (in sets)

Does not matter; {a, b} = {b, a}.

Repeated elements (in sets)

Ignored; {a, a, b} = {a, b}.

Z (Integers)

The set of all integers, including positive, negative, and zero.

Z+ (Positive Integers)

The set of positive integers = {1, 2, 3, 4, …}.

N (Natural Numbers)

The set of all natural numbers = {0, 1, 2, 3, 4, …}.

Q (Rational Numbers)

The set of all numbers that can be expressed as a/b, where a and b are integers and b ≠ 0.

R (Real Numbers)

The set of all real numbers.

Roster Notation

A way to specify a set by listing elements with curly braces, e.g., {1, 3, 5, 9} or {1, 3, 5, …, 99}.

Set Builder Notation

A way to specify a set by describing a property its elements satisfy, e.g., {x Î S: some property x satisfies}.

Infinite Set

A set with an infinite number of elements.

Finite Set

A set with a finite number of elements.

Cardinality of a Set (|S|)

The number of elements in a finite set S.

Empty Set (∅ or {})

The set with no elements.

Cardinality of an Empty Set

The number of elements in an empty set, which is 0.

Intersection of Two Sets (A ∩ B)

The set of all elements which belong to both set A and set B.

Union of Two Sets (A ∪ B)

The set of all elements which belong to set A or set B or both.

Difference Between Two Sets (A - B)

The set of elements which belong to set A but not belong to set B.

Complement of a Set (A')

The set of elements which belong to the universal set U but not to set A.

Symmetric Difference (A Å B)

The set of elements which belong to A or B but NOT both (A ∪ B - A ∩ B).

Subset (A ⊆ B)

If every element of set A is also an element of set B, then A is called a subset of B.

Set of Sets

A set that may contain other sets as its elements.

Power Set (P(A))

The set of all subsets of a set A.

Cardinality of a Power Set

If a set has n elements, the cardinality of its power set is 2ⁿ.

Set Identity

An equation involving sets that is true regardless of the contents of the sets in the expression.