Unit 2 - Sets and Predicate Logic Flashcards
What does the symbol ∅ denote
An empty set.
If |A| = 1, we say that A is
a singleton set
A set is
an unordered collection of distinct objects.
What does the symbol \ represent
Difference
a ∈ A
a is in A
is True if and only if a is an element of the set A
There are two main ways to formally define a set
Definition by enumeration
Definition by set-builder notation
{x ∈ A | x > 2 ∧ x < 4}
the vertical line “|” is read as
“such that” or “where”;
{x ∈ A | x > 2 ∧ x < 4}
what appears on the left of “|”
represents an element of the set (in this example, x) and its origin (in this example, x must be an element of A)
{x ∈ A | x > 2 ∧ x < 4}
what appears on the right of “|”
provides a condition that must be satisfied
by each element of the set
{x ∈ A | x > 2 ∧ x < 4}
Explain the above in words and the resulting set in {} notation.
B is the set containing all elements x in set A,
such that x is greater than 2, and x is smaller than 4
Therefore, B is the singleton set {3}.
The symbol B often used in set notation represents
the set of truth values (also called Boolean values) {True, False}
The symbol N often used in set notation represents
the set of natural numbers {0, 1, 2, 3, . . .}
The symbol Z often used in set notation represents
the set of the integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .}
The symbol Q often used in set notation represents
the set of the rational numbers
The symbol R often used in Set notation represents
the set of the real numbers
