Discrete Mathematics and Its
Applications - Chapter 1 with Complete
Solutions
What is the definition of a set in discrete mathematics?
✔✔A set is a collection of distinct objects considered as an object in its own right.
What is the difference between a subset and a proper subset?
✔✔A subset contains some or all elements of a set, while a proper subset contains some but not
all elements of a set.
How is the union of two sets defined?
✔✔The union of two sets includes all elements from both sets, with duplicates removed.
What does the intersection of two sets represent?
✔✔The intersection of two sets includes only the elements that are common to both sets.
What is the cardinality of a set?
✔✔The cardinality of a set is the number of elements in the set.
1
,What is the power set of a set?
✔✔The power set of a set is the set of all possible subsets of the original set.
What is the difference between a finite set and an infinite set?
✔✔A finite set has a limited number of elements, while an infinite set has an unlimited number
of elements.
What is the complement of a set?
✔✔The complement of a set consists of all elements that are not in the set but are in the
universal set.
What is a Venn diagram used for in discrete mathematics?
✔✔A Venn diagram is used to visually represent sets and their relationships to each other.
What is a universal set in discrete mathematics?
✔✔A universal set contains all the elements under consideration for a particular problem or
context.
2
, How is a Cartesian product of two sets defined?
✔✔The Cartesian product of two sets is the set of all ordered pairs where the first element is
from the first set and the second element is from the second set.
What is a function in the context of discrete mathematics?
✔✔A function is a relation between two sets where every element in the first set is associated
with exactly one element in the second set.
What does it mean for a function to be one-to-one (injective)?
✔✔A function is one-to-one if each element of the domain maps to a unique element in the
codomain.
What is the difference between a surjective and an injective function?
✔✔A surjective function maps every element of the codomain to at least one element in the
domain, while an injective function maps each element of the domain to a unique element in the
codomain.
What is the composition of two functions?
3
Applications - Chapter 1 with Complete
Solutions
What is the definition of a set in discrete mathematics?
✔✔A set is a collection of distinct objects considered as an object in its own right.
What is the difference between a subset and a proper subset?
✔✔A subset contains some or all elements of a set, while a proper subset contains some but not
all elements of a set.
How is the union of two sets defined?
✔✔The union of two sets includes all elements from both sets, with duplicates removed.
What does the intersection of two sets represent?
✔✔The intersection of two sets includes only the elements that are common to both sets.
What is the cardinality of a set?
✔✔The cardinality of a set is the number of elements in the set.
1
,What is the power set of a set?
✔✔The power set of a set is the set of all possible subsets of the original set.
What is the difference between a finite set and an infinite set?
✔✔A finite set has a limited number of elements, while an infinite set has an unlimited number
of elements.
What is the complement of a set?
✔✔The complement of a set consists of all elements that are not in the set but are in the
universal set.
What is a Venn diagram used for in discrete mathematics?
✔✔A Venn diagram is used to visually represent sets and their relationships to each other.
What is a universal set in discrete mathematics?
✔✔A universal set contains all the elements under consideration for a particular problem or
context.
2
, How is a Cartesian product of two sets defined?
✔✔The Cartesian product of two sets is the set of all ordered pairs where the first element is
from the first set and the second element is from the second set.
What is a function in the context of discrete mathematics?
✔✔A function is a relation between two sets where every element in the first set is associated
with exactly one element in the second set.
What does it mean for a function to be one-to-one (injective)?
✔✔A function is one-to-one if each element of the domain maps to a unique element in the
codomain.
What is the difference between a surjective and an injective function?
✔✔A surjective function maps every element of the codomain to at least one element in the
domain, while an injective function maps each element of the domain to a unique element in the
codomain.
What is the composition of two functions?
3
