Sets and Functions: An Introduction to
Mathematical Concepts Exam 2026
Questions and Answers
mathematical function - Correct answer-a relation that assigns to each element of a
set exactly one element of another set.
element (∈) - Correct answer-a member of a set.
natural numbers (N) - Correct answer-the set {0, 1, 2, 3, ...}.
rational numbers (Q) - Correct answer-numbers that can be expressed as the
quotient of two integers.
real numbers (R) - Correct answer-all the numbers on the number line, including
both rational and irrational numbers.
integers (Z) - Correct answer-the set of whole numbers, including negative
numbers, zero, and positive numbers.
set-builder notation - Correct answer-a notation used to describe a set by stating the
properties that its members must satisfy.
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,A equals B (=) - Correct answer-a statement indicating that two sets or quantities
are identical.
A is a (proper) subset of B (⊂) - Correct answer-a set A is a proper subset of set B
if all elements of A are in B and A is not equal to B.
A is a superset of B (⊇) - Correct answer-a set A is a superset of set B if it contains
all elements of B.
the union of A and B (∪) - Correct answer-the set containing all elements that are
in A, in B, or in both.
the intersection of A and B (∩) - Correct answer-the set containing all elements that
are both in A and in B.
Cartesian product of A and B (×) - Correct answer-the set of all ordered pairs (a, b)
where a is in A and b is in B.
domain of the variable - Correct answer-the set of all possible input values for a
function.
abstract objects - Correct answer-concepts or entities that do not have a physical
existence but are used in mathematical reasoning.
culturally literate - Correct answer-having knowledge and understanding of various
cultural contexts and practices.
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,mathematician - Correct answer-a person who specializes in the field of
mathematics.
mathematical theory - Correct answer-a system of ideas and principles that explain
mathematical concepts and relationships.
written explanations - Correct answer-descriptions or clarifications of
mathematical concepts expressed in complete sentences.
defined terms - Correct answer-specific words or phrases that have been given
precise meanings within a mathematical context.
incomplete grasp of definitions - Correct answer-a lack of full understanding of the
meanings of terms, which can hinder comprehension.
set - Correct answer-a collection of distinct objects considered as a whole.
N+ - Correct answer-the set {1, 2, 3, ...}, representing natural numbers excluding
zero.
Element - Correct answer-When x is a member of set X, we say that x is an
element of X, denoted as x ∈ X.
Not an Element - Correct answer-When x is not a member of set X, we write x /∈
X.
Natural Numbers - Correct answer-The set of positive integers, denoted by N.
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, Set Membership Notation - Correct answer-A shorthand notation to express
membership in a set, e.g., '4 ∈ N' means '4 is in the set of natural numbers'.
Multiple Elements Notation - Correct answer-To express that multiple elements are
members of the same set, we can write '2, 4 ∈ N' to mean '2 ∈ N and 4 ∈ N'.
Explicit Set Definition - Correct answer-A set can be defined by listing its elements
explicitly, e.g., {1, 3, 5, 7} is the set of the first four odd numbers.
Set Order Irrelevance - Correct answer-The order of elements in a set does not
matter; {1, 3, 5, 7} is the same as {1, 5, 3, 7}.
Set Repetition Irrelevance - Correct answer-Repeating elements in a set does not
matter; {1, 3, 5, 7} is the same as {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7}.
Pattern Identification in Sets - Correct answer-For large sets, we provide enough
information for the reader to identify a pattern for determining membership.
Standard Set Names - Correct answer-Some sets have standard names and
notations, such as the integers denoted by Z.
Integers - Correct answer-The elements of the set {. . . , −3, −2, −1, 0, 1, 2, 3, . . .},
denoted by Z.
Rational Numbers - Correct answer-The elements of the set {p/q | p, q ∈ Z and q ≠
0}, denoted by Q.
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Mathematical Concepts Exam 2026
Questions and Answers
mathematical function - Correct answer-a relation that assigns to each element of a
set exactly one element of another set.
element (∈) - Correct answer-a member of a set.
natural numbers (N) - Correct answer-the set {0, 1, 2, 3, ...}.
rational numbers (Q) - Correct answer-numbers that can be expressed as the
quotient of two integers.
real numbers (R) - Correct answer-all the numbers on the number line, including
both rational and irrational numbers.
integers (Z) - Correct answer-the set of whole numbers, including negative
numbers, zero, and positive numbers.
set-builder notation - Correct answer-a notation used to describe a set by stating the
properties that its members must satisfy.
©COPYRIGHT 2025, ALL RIGHTS RESERVED 1
,A equals B (=) - Correct answer-a statement indicating that two sets or quantities
are identical.
A is a (proper) subset of B (⊂) - Correct answer-a set A is a proper subset of set B
if all elements of A are in B and A is not equal to B.
A is a superset of B (⊇) - Correct answer-a set A is a superset of set B if it contains
all elements of B.
the union of A and B (∪) - Correct answer-the set containing all elements that are
in A, in B, or in both.
the intersection of A and B (∩) - Correct answer-the set containing all elements that
are both in A and in B.
Cartesian product of A and B (×) - Correct answer-the set of all ordered pairs (a, b)
where a is in A and b is in B.
domain of the variable - Correct answer-the set of all possible input values for a
function.
abstract objects - Correct answer-concepts or entities that do not have a physical
existence but are used in mathematical reasoning.
culturally literate - Correct answer-having knowledge and understanding of various
cultural contexts and practices.
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,mathematician - Correct answer-a person who specializes in the field of
mathematics.
mathematical theory - Correct answer-a system of ideas and principles that explain
mathematical concepts and relationships.
written explanations - Correct answer-descriptions or clarifications of
mathematical concepts expressed in complete sentences.
defined terms - Correct answer-specific words or phrases that have been given
precise meanings within a mathematical context.
incomplete grasp of definitions - Correct answer-a lack of full understanding of the
meanings of terms, which can hinder comprehension.
set - Correct answer-a collection of distinct objects considered as a whole.
N+ - Correct answer-the set {1, 2, 3, ...}, representing natural numbers excluding
zero.
Element - Correct answer-When x is a member of set X, we say that x is an
element of X, denoted as x ∈ X.
Not an Element - Correct answer-When x is not a member of set X, we write x /∈
X.
Natural Numbers - Correct answer-The set of positive integers, denoted by N.
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, Set Membership Notation - Correct answer-A shorthand notation to express
membership in a set, e.g., '4 ∈ N' means '4 is in the set of natural numbers'.
Multiple Elements Notation - Correct answer-To express that multiple elements are
members of the same set, we can write '2, 4 ∈ N' to mean '2 ∈ N and 4 ∈ N'.
Explicit Set Definition - Correct answer-A set can be defined by listing its elements
explicitly, e.g., {1, 3, 5, 7} is the set of the first four odd numbers.
Set Order Irrelevance - Correct answer-The order of elements in a set does not
matter; {1, 3, 5, 7} is the same as {1, 5, 3, 7}.
Set Repetition Irrelevance - Correct answer-Repeating elements in a set does not
matter; {1, 3, 5, 7} is the same as {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7}.
Pattern Identification in Sets - Correct answer-For large sets, we provide enough
information for the reader to identify a pattern for determining membership.
Standard Set Names - Correct answer-Some sets have standard names and
notations, such as the integers denoted by Z.
Integers - Correct answer-The elements of the set {. . . , −3, −2, −1, 0, 1, 2, 3, . . .},
denoted by Z.
Rational Numbers - Correct answer-The elements of the set {p/q | p, q ∈ Z and q ≠
0}, denoted by Q.
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