WGU C960 DISCRETE MATH II ACTUAL
TEST PAPER COMPLETE QUESTIONS AND
ANSWERS FULL SOLUTION
●● When counting the cardinality of a set whose elements include other
sets, how is each inner set counted?
Answer: Each set contained within the outer set counts as a single
element, regardless of how many elements that inner set itself contains.
(Section 2.2)
●● Is the empty set the same thing as a set containing only the empty set
as its single element?
Answer: No, the empty set has a cardinality of 0, while a set containing
only the empty set as its one element has a cardinality of 1. (Section 2.2)
●● What is the difference between using the "is an element of" symbol
(∈) versus the "is a subset of" symbol (⊆) when relating a set to another
set of sets?
Answer: The element symbol is used when the set in question is literally
one of the listed members of the outer set, while the subset symbol is
used when every member of the set in question is also a member of the
outer set. (Section 2.2)
,●● Can a set contain a mix of individual numbers and sets of numbers as
its elements?
Answer: Yes, a single set can contain a combination of plain numbers
and other sets as its elements at the same time. (Section 2.2)
●● What is the power set of a set A?
Answer: The set of all subsets of A, including the empty set and A itself.
(Section 2.2)
●● What notation is commonly used to denote the power set of a set A?
Answer: P(A). (Section 2.2)
●● According to the theorem on the cardinality of a power set, if a finite
set A has cardinality n, what is the cardinality of its power set?
Answer: 2 raised to the power of n. (Section 2.2)
●● Why does the empty set always appear as an element of the power
set of any set?
Answer: Because the empty set is considered a subset of every set, so it
must be included among the subsets that make up the power set. (Section
2.2)
●● Why does a set A always appear as an element of its own power set,
P(A)?
,Answer: Because a set is always considered a subset of itself, so A itself
must be included among the subsets that make up the power set. (Section
2.2)
●● If a set has 4 elements, how many total subsets does it have,
including the empty set and the full set itself?
Answer: 16 subsets, since 2 raised to the power of 4 equals 16. (Section
2.2)
●● When listing out the elements of a power set of a set with several
elements, why is it helpful to organize the subsets by size?
Answer: Organizing subsets by size, such as listing all subsets of size 0,
then size 1, then size 2, and so on, makes it easier to systematically
ensure that every possible subset has been accounted for without missing
or repeating any. (Section 2.2)
●● What is the intersection of two sets A and B?
Answer: The set of all elements that are elements of both A and B.
(Section 2.3)
●● How is the intersection of sets A and B denoted, and how is it read
aloud?
Answer: It is denoted A ∩ B, read as "A intersect B." (Section 2.3)
●● What is the union of two sets A and B?
, Answer: The set of all elements that are elements of A or B. (Section
2.3)
●● How is the union of sets A and B denoted, and how is it read aloud?
Answer: It is denoted A ∪ B, read as "A union B." (Section 2.3)
●● Does the definition of union use the inclusive or or the exclusive or?
Answer: The inclusive or, meaning that if an element belongs to both A
and B, it is still included as a single element in the union. (Section 2.3)
●● Can the intersection and union operations be applied to infinite sets,
not just finite ones?
Answer: Yes, both the intersection and union operations can be applied
to infinite sets, such as sets defined by properties like being multiples of
a certain number. (Section 2.3)
●● Why is it important to use parentheses when combining more than
one set operation, such as in an expression involving both union and
intersection?
Answer: Because the order in which different types of operations, like
union and intersection, are applied can change the resulting set, so
parentheses are needed to make the intended order of operations clear.
(Section 2.3)
TEST PAPER COMPLETE QUESTIONS AND
ANSWERS FULL SOLUTION
●● When counting the cardinality of a set whose elements include other
sets, how is each inner set counted?
Answer: Each set contained within the outer set counts as a single
element, regardless of how many elements that inner set itself contains.
(Section 2.2)
●● Is the empty set the same thing as a set containing only the empty set
as its single element?
Answer: No, the empty set has a cardinality of 0, while a set containing
only the empty set as its one element has a cardinality of 1. (Section 2.2)
●● What is the difference between using the "is an element of" symbol
(∈) versus the "is a subset of" symbol (⊆) when relating a set to another
set of sets?
Answer: The element symbol is used when the set in question is literally
one of the listed members of the outer set, while the subset symbol is
used when every member of the set in question is also a member of the
outer set. (Section 2.2)
,●● Can a set contain a mix of individual numbers and sets of numbers as
its elements?
Answer: Yes, a single set can contain a combination of plain numbers
and other sets as its elements at the same time. (Section 2.2)
●● What is the power set of a set A?
Answer: The set of all subsets of A, including the empty set and A itself.
(Section 2.2)
●● What notation is commonly used to denote the power set of a set A?
Answer: P(A). (Section 2.2)
●● According to the theorem on the cardinality of a power set, if a finite
set A has cardinality n, what is the cardinality of its power set?
Answer: 2 raised to the power of n. (Section 2.2)
●● Why does the empty set always appear as an element of the power
set of any set?
Answer: Because the empty set is considered a subset of every set, so it
must be included among the subsets that make up the power set. (Section
2.2)
●● Why does a set A always appear as an element of its own power set,
P(A)?
,Answer: Because a set is always considered a subset of itself, so A itself
must be included among the subsets that make up the power set. (Section
2.2)
●● If a set has 4 elements, how many total subsets does it have,
including the empty set and the full set itself?
Answer: 16 subsets, since 2 raised to the power of 4 equals 16. (Section
2.2)
●● When listing out the elements of a power set of a set with several
elements, why is it helpful to organize the subsets by size?
Answer: Organizing subsets by size, such as listing all subsets of size 0,
then size 1, then size 2, and so on, makes it easier to systematically
ensure that every possible subset has been accounted for without missing
or repeating any. (Section 2.2)
●● What is the intersection of two sets A and B?
Answer: The set of all elements that are elements of both A and B.
(Section 2.3)
●● How is the intersection of sets A and B denoted, and how is it read
aloud?
Answer: It is denoted A ∩ B, read as "A intersect B." (Section 2.3)
●● What is the union of two sets A and B?
, Answer: The set of all elements that are elements of A or B. (Section
2.3)
●● How is the union of sets A and B denoted, and how is it read aloud?
Answer: It is denoted A ∪ B, read as "A union B." (Section 2.3)
●● Does the definition of union use the inclusive or or the exclusive or?
Answer: The inclusive or, meaning that if an element belongs to both A
and B, it is still included as a single element in the union. (Section 2.3)
●● Can the intersection and union operations be applied to infinite sets,
not just finite ones?
Answer: Yes, both the intersection and union operations can be applied
to infinite sets, such as sets defined by properties like being multiples of
a certain number. (Section 2.3)
●● Why is it important to use parentheses when combining more than
one set operation, such as in an expression involving both union and
intersection?
Answer: Because the order in which different types of operations, like
union and intersection, are applied can change the resulting set, so
parentheses are needed to make the intended order of operations clear.
(Section 2.3)
