CPE 1201 - Discrete Mathematics Lecture Notes

A collection of question and answer formatted flashcards based on the key concepts in the lecture notes for Discrete Mathematics.

What is a set?

An unordered collection of objects called elements or members.

What does a ∈ A indicate?

It denotes that 'a' is an element of set A.

What does a ∉ A indicate?

It denotes that 'a' is not an element of set A.

What is the Roster Method?

It lists all the members of a set when possible, enclosed in braces.

What is Set Builder Notation?

It characterizes elements in the set by stating properties they must have.

What is the set of natural numbers denoted by?

N = {0, 1, 2, 3, …}.

What does the notation A ⊆ B mean?

It indicates that set A is a subset of set B.

What defines A being a proper subset of B?

A is a proper subset of B if A ⊆ B and there exists an element in B that is not in A.

What is the Cartesian product of sets A and B?

It is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, denoted by A × B.

What is the power set of a set S?

The power set P(S) is the set of all subsets of S.

What does |S| denote?

It denotes the cardinality of set S, representing the number of distinct elements in S.

What is the empty set?

A set that has no elements, denoted by ∅ or {}.

What is a singleton set?

A set that has only one element, such as {∅}, which is not an empty set.

Who created the graphical representation of sets known as Venn Diagrams?

John Venn in 1881.

What is the importance of a truth set in discrete mathematics?

It is the set of elements in a given domain for which a predicate is true.

What does ∀x∈R (x² ≥ 0) mean?

The square of every real number is nonnegative.

What is an example of a truth set for Q(x) where Q(x) is x² = 2?

The truth set is the empty set, as there are no integers for which x² = 2.