Chapter 2 Flashcards
elements
objects in a set
singleton set
contains only one element
empty set
also called null set
contains no elements
denoted by 0
C
the set of all complex numbers
R+
the set of all positive real numbers
R
the set of all real numbers
Z+
the set of all positive integers (does NOT include 0)
Z
the set of all integers
set
an unordered collection of distinct objects
intersection of a collection
the set that contains those elements that are members of all the sets in the collection
union of a collection
the set that contains those elements that are members of at least one set in the collection
intersection
A n B
contains those elements in both A and B
union
A u B
contains those elements in either A or B
P(S)
the power set of S
the set of all subsets of the set S
if n is the number of elements in S, the the power set contains 2^n elements
|S|
cardinality of S
length of a finite set
a E A
a is an element of A
B >= A
B is a superset of A
paradoxes
logical inconsistencies
A - B
difference
complement of B with respect to A
the set containing those elements that are in A but not in B
A X B
Cartesian product
the set of all ordered pairs (a,b), where a E A and b E B
roster method
list all members of the set within {}
set builder notation
characterize all the elements in a set by stating the property or properties they must have
N
the set of all natural numbers (includes 0)
intervals
sets of all real numbers between two numbers a and b, with or without a and b
A <= B
A is a subset of B
Ax(x E A –> x E B)
A < B
A is a proper subset of B
Ax(x E A –x E B) && Ex(x E B && x !E A)
A bar
complement of A with respect to the universal set U
U - A
multiset
an unordered collection of elements where on element can occur as a member more than once
disjoint
two sets are disjoint if their intersection is the empty set
truth set
the set of elements x in the domain D for which a predicate P(x) is true
relation
a subset of A X B
Q
the set of all rational numbers
{p/q | p E Z, q E Z, and q != 0}
