MATH 1100 || 100% verified solutions.
The set {California, Colorado, Connecticut} is expressed using _______________. The set {x|x
is a U.S.state whose name begins with the letter C} is expressed using ________________.
correct answers the roster method ; the roster method.
A set that contains no elements is called the _______ set and is represented by _______. correct
answers empty/null ; Ø = { }
The symbol
∈ is used to indicate that an object is an _________________ of a set. correct answers element
The set of {1,2,3,4,5} is called the set of ____________. correct answers natural numbers
Two sets that contain the same number of elements are called _______. correct answers
equivalent
Two sets that contain exactly the same elements are called __________ sets correct answers
equal
the collection of current NFL players
the collection of US airports correct answers The collection is well defined and therefore it is a
set.
Cancer and Capricorn
Tuesday and Thursday correct answers the set of zodiac signs that begin with C
the set of weekdays that begin with T
{15, 16, 17, 18,....} correct answers all natural numbers greater than 14
,A is the set of cities in a regions B is the set of people who are now mayors of the cities in that
region correct answers The sets are equivalent because they
contain the same number of elements.
The sets are not equal because they do not contain the exact same elements.
A = {2,2,2,4,4,6,8,10}
B = {10,8,6,4,2} correct answers The sets are equivalent because n(A)=n(B)
The sets are equal because set A contains the exact same elements as set B.
Visual relationships among sets are shown by correct answers Venn diagrams
The set of all elements in the universal set that are not in set A is called the _________ of set A,
and is symbolized by _________. correct answers complement ; A'
The set of elements common to both set A and set B is called the __________ of sets A and B,
and is symbolized by __________ correct answers intersection; A ∩ B
The set of elements that are members of set A or set B or of both sets is called the _________ of
sets A and B, and is symbolized by _________. correct answers union ; A∪B
The formula for the cardinal number of elements in set A or set B is n(A∪B)= correct answers
n(A) + n(B) - n(A∪B)
Disjoint sets are represented by circles that do not overlap. correct answers the statement is true
If set A is a proper subset of set B, the sets are represented by two circles where circle A is drawn
outside of circle B. correct answers The statement is false. If set A is a proper subset of set B, the
sets are represented by two circles where circle A is drawn inside of circle B.
,Equal sets are represented by the same circle. correct answers The statement is true.
As the number of elements in a set increases, larger circles are needed to represent the set.
correct answers False, the size of a circle does not need to be proportional to the number of
elements in its corresponding set.
In order to perform set operations such as
(A ∪ B) ∩ (A ∪ C), begin by performing any set operations ________ correct answers inside
parentheses
The three sets in the Venn diagram will separate the universal set into ____ regions correct
answers 8
It can be proved that
(A∩B)′=A′∪B′, so this means that the complement of the intersection of two sets is the union of
the complement of those sets correct answers The statement is true because a theorem is always
true and
(A∩B)′=A′∪B′ means that the complement of the intersection of two sets is the union of the
complement of those sets.
A statement is a sentence that is _______ or _______, but not both simultaneously. correct
answers true ; false
The negation of a true statement is a ____________ statement and the negation of a false
statement is a ____________ statement. correct answers false ; true
The negation of statement p is expressed by writing _______. We read this as _______. correct
answers ~p ; not p
, Statements that contain the words
all,some, and no are called ________________ statements. correct answers quantified
The statement "All A are B" can be expressed equivalently as _______. correct answers There
are no A that are not B.
What can the statement "Some A are B" be expressed equivalently as? correct answers There
exists at least one A that is a B.
The statement "No A are B" can be expressed equivalently as _______. correct answers All A are
not B.
What can the statement "Some A are not B" be expressed equivalently as? correct answers Not
all A are B.
The negation of "All A are B" is _______. correct answers Some A are not B.
What is the negation of "Some A are B"? correct answers No A are B.
Some women have served as U.S. senators is a statement correct answers Yes, because the
sentence can be either true or false, but not both simultaneously.
Stacy ate all of her spinach is a statement correct answers yes, because it could be labeled as true
or false
take a right at Cross Street
is a statement? correct answers no, because it is a command
The set {California, Colorado, Connecticut} is expressed using _______________. The set {x|x
is a U.S.state whose name begins with the letter C} is expressed using ________________.
correct answers the roster method ; the roster method.
A set that contains no elements is called the _______ set and is represented by _______. correct
answers empty/null ; Ø = { }
The symbol
∈ is used to indicate that an object is an _________________ of a set. correct answers element
The set of {1,2,3,4,5} is called the set of ____________. correct answers natural numbers
Two sets that contain the same number of elements are called _______. correct answers
equivalent
Two sets that contain exactly the same elements are called __________ sets correct answers
equal
the collection of current NFL players
the collection of US airports correct answers The collection is well defined and therefore it is a
set.
Cancer and Capricorn
Tuesday and Thursday correct answers the set of zodiac signs that begin with C
the set of weekdays that begin with T
{15, 16, 17, 18,....} correct answers all natural numbers greater than 14
,A is the set of cities in a regions B is the set of people who are now mayors of the cities in that
region correct answers The sets are equivalent because they
contain the same number of elements.
The sets are not equal because they do not contain the exact same elements.
A = {2,2,2,4,4,6,8,10}
B = {10,8,6,4,2} correct answers The sets are equivalent because n(A)=n(B)
The sets are equal because set A contains the exact same elements as set B.
Visual relationships among sets are shown by correct answers Venn diagrams
The set of all elements in the universal set that are not in set A is called the _________ of set A,
and is symbolized by _________. correct answers complement ; A'
The set of elements common to both set A and set B is called the __________ of sets A and B,
and is symbolized by __________ correct answers intersection; A ∩ B
The set of elements that are members of set A or set B or of both sets is called the _________ of
sets A and B, and is symbolized by _________. correct answers union ; A∪B
The formula for the cardinal number of elements in set A or set B is n(A∪B)= correct answers
n(A) + n(B) - n(A∪B)
Disjoint sets are represented by circles that do not overlap. correct answers the statement is true
If set A is a proper subset of set B, the sets are represented by two circles where circle A is drawn
outside of circle B. correct answers The statement is false. If set A is a proper subset of set B, the
sets are represented by two circles where circle A is drawn inside of circle B.
,Equal sets are represented by the same circle. correct answers The statement is true.
As the number of elements in a set increases, larger circles are needed to represent the set.
correct answers False, the size of a circle does not need to be proportional to the number of
elements in its corresponding set.
In order to perform set operations such as
(A ∪ B) ∩ (A ∪ C), begin by performing any set operations ________ correct answers inside
parentheses
The three sets in the Venn diagram will separate the universal set into ____ regions correct
answers 8
It can be proved that
(A∩B)′=A′∪B′, so this means that the complement of the intersection of two sets is the union of
the complement of those sets correct answers The statement is true because a theorem is always
true and
(A∩B)′=A′∪B′ means that the complement of the intersection of two sets is the union of the
complement of those sets.
A statement is a sentence that is _______ or _______, but not both simultaneously. correct
answers true ; false
The negation of a true statement is a ____________ statement and the negation of a false
statement is a ____________ statement. correct answers false ; true
The negation of statement p is expressed by writing _______. We read this as _______. correct
answers ~p ; not p
, Statements that contain the words
all,some, and no are called ________________ statements. correct answers quantified
The statement "All A are B" can be expressed equivalently as _______. correct answers There
are no A that are not B.
What can the statement "Some A are B" be expressed equivalently as? correct answers There
exists at least one A that is a B.
The statement "No A are B" can be expressed equivalently as _______. correct answers All A are
not B.
What can the statement "Some A are not B" be expressed equivalently as? correct answers Not
all A are B.
The negation of "All A are B" is _______. correct answers Some A are not B.
What is the negation of "Some A are B"? correct answers No A are B.
Some women have served as U.S. senators is a statement correct answers Yes, because the
sentence can be either true or false, but not both simultaneously.
Stacy ate all of her spinach is a statement correct answers yes, because it could be labeled as true
or false
take a right at Cross Street
is a statement? correct answers no, because it is a command
