WGU C959 Discrete Mathematics I Exam Study Guide |
2026/2027 Edition | 200 Verified Questions
WGU C959 Discrete Mathematics I Exam 2026-2027 QUESTIONS AND ANSWERS ALREADY GRADED A+.
100% Verified Solutions | Updated Per Latest Guidelines | Graded A+
This comprehensive study guide for WGU C959 Discrete Mathematics I is meticulously crafted to
align with the 2026/2027 academic year curriculum. It features 200 verified questions with correct
solutions, covering all essential topics including logic, set theory, functions, algorithms, and graph
theory. Designed to ensure exam success, this guide provides clear rationales and is updated to reflect
the latest guidelines. It is an indispensable resource for students aiming to excel in the WGU C959
final exam.
Key Features:
Logic and propositional equivalences
Set theory and operations
Functions, sequences, and summations
Algorithms and complexity analysis
Graph theory and trees
Mathematical induction and recursion
Updates for 2026:
- Updated to reflect 2026/2027 WGU C959 curriculum changes
- Revised answer rationales for clarity and accuracy
- Added new practice questions based on recent exam patterns
- Enhanced explanations for complex topics like graph theory
- Aligned with latest WGU assessment objectives
Abstract:
This study guide is an authoritative resource for students preparing for the WGU C959 Discrete Mathematics I
examination. It consolidates 200 verified questions and solutions, meticulously organized to mirror the exam's
structure and content. The guide covers fundamental discrete mathematics concepts, including logic, set theory,
functions, algorithms, and graph theory, with a focus on application and problem-solving. Each question is
accompanied by a detailed rationale, explaining the correct answer and common misconceptions. The content is
updated to align with the 2026/2027 academic year, ensuring relevance and accuracy. This guide is designed to
facilitate deep understanding and retention, making it an essential tool for achieving a high score. It also includes
strategic tips for tackling exam questions and managing time effectively. By using this guide, students can
confidently approach the exam, knowing they have mastered the core material.
Keywords:
Discrete Mathematics, WGU C959, Exam Study Guide, Logic and Proofs, Set Theory, Graph Theory, Algorithms,
Verified Solutions
Answer Format:
Each question is presented in a multiple-choice format, followed by the correct answer and a comprehensive
rationale. The rationale explains why the correct answer is right and why the distractors are incorrect, reinforcing
key concepts. This format aids in understanding the underlying principles and improves retention.
Compliance Checklist:
All questions are verified against WGU C959 course objectives
Solutions are accurate and aligned with latest academic standards
Page 1
, Content is updated for the 2026/2027 academic year
Rationales are clear and pedagogically sound
Format matches the official exam style
Content Area Overview:
Content Area Questions Key Topics Weight
Logic and Proofs 1-30 Propositional logic, truth tables, logical 15%
equivalences, predicates, quantifiers, proof
techniques
Set Theory 31-60 Sets, subsets, operations, Venn diagrams, 15%
cardinality, power sets, Cartesian products
Functions, Sequences, and 61-90 Functions, injective/surjective/bijective, 15%
Summations composition, inverse, sequences,
summations, growth of functions
Algorithms and Complexity 91-120 Algorithm definition, searching/sorting, 15%
Big-O notation, complexity classes,
recursion
Graph Theory and Trees 121-160 Graph models, terminology, connectivity, 20%
Euler/Hamilton paths, planar graphs, trees,
spanning trees
Induction and Recursion 161-200 Mathematical induction, strong induction, 20%
recursive definitions, recursive algorithms,
structural induction
Page 2
,Q1. Which of the following sets is equinumerous with the power set of the set of
natural numbers?
A. The set of all finite subsets of the natural numbers
B. The set of all functions from the natural numbers to {0,1}
C. The set of all rational numbers
D. The set of all finite sequences of natural numbers
Correct Answer: B. The set of all functions from the natural numbers to {0,1}
Rationale: The power set of the natural numbers has cardinality 2^!50, which is
uncountable. The set of all functions from to {0,1} also has cardinality 2^0, as each
function corresponds to a subset via its indicator function. The other options are all
countable sets.
Why Wrong:
A - The set of finite subsets of is countable, not uncountable.
C - The rationals are countable, so they cannot be equinumerous with the power set of
.
D - The set of finite sequences of natural numbers is countable.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 2.5
Q2. Consider the logical statement: (p -> q) (q -> r). Which of the following is
logically equivalent to its negation?
A. p ¬q r
B. ¬p q ¬r
C. (p ¬q) (q ¬r)
D. ¬(p -> q) ¬(q -> r)
Correct Answer: D. ¬(p -> q) ¬(q -> r)
Rationale: By De Morgan's law, the negation of a conjunction is the disjunction of the
negations. Thus ¬[(p -> q) (q -> r)] ¬(p -> q) ¬(q -> r). Option C is equivalent to the
same because ¬(p -> q) p ¬q and ¬(q -> r) q ¬r, but D is the direct application.
Why Wrong:
A - This represents a specific case, not the full negation.
B - This is not logically equivalent to the negation.
C - This is logically equivalent but not the direct negation form; D is the correct direct
form.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 1.3
Q3. Which of the following relations on the set of integers is an equivalence relation?
A. R = {(a,b) | a + b is even}
B. R = {(a,b) | a - b is odd}
C. R = {(a,b) | a b}
Page 3
, D. R = {(a,b) | a divides b}
Correct Answer: A. R = {(a,b) | a + b is even}
Rationale: The relation 'a + b is even' is reflexive (a+a is even), symmetric (a+b = b+a),
and transitive (if a+b even and b+c even, then a and c have same parity as b, so a+c
even). The others fail transitivity or symmetry.
Why Wrong:
B - This relation is not reflexive because a - a = 0 is even, not odd.
C - This relation is not symmetric (e.g., 1 2 but 2 1 is false).
D - This relation is not symmetric (e.g., 2 divides 4 but 4 does not divide 2).
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 9.5
Q4. How many onto functions are there from a set with 5 elements to a set with 3
elements?
A. 150
B. 243
C. 60
D. 90
Correct Answer: A. 150
Rationale: The number of onto functions from an m-element set to an n-element set is n! *
S(m,n), where S(m,n) is a Stirling number of the second kind. For m=5, n=3, S(5,3)=25, so
3! * 25 = 6 * 25 = 150. Alternatively, inclusion-exclusion: 3^5 - C(3,1)*2^5 + C(3,2)*1^5
= 243 - 96 + 3 = 150.
Why Wrong:
B - 243 is the total number of functions from a 5-element set to a 3-element set (3^5),
not onto.
C - 60 might result from miscounting or using permutations only.
D - 90 is not the correct count; it might come from an incorrect inclusion-exclusion
calculation.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 6.1
Q5. Which of the following statements is true about the sequence defined by a_n =
3a_{n-1} - 2a_{n-2} with a_0 = 2 and a_1 = 3?
A. The sequence is eventually periodic with period 2.
B. The closed form is a_n = 1 + 2^n.
C. The sequence grows exponentially with base 3.
D. The sequence satisfies a_n = 2^n + 1 for all n 0.
Correct Answer: D. The sequence satisfies a_n = 2^n + 1 for all n 0.
Page 4
2026/2027 Edition | 200 Verified Questions
WGU C959 Discrete Mathematics I Exam 2026-2027 QUESTIONS AND ANSWERS ALREADY GRADED A+.
100% Verified Solutions | Updated Per Latest Guidelines | Graded A+
This comprehensive study guide for WGU C959 Discrete Mathematics I is meticulously crafted to
align with the 2026/2027 academic year curriculum. It features 200 verified questions with correct
solutions, covering all essential topics including logic, set theory, functions, algorithms, and graph
theory. Designed to ensure exam success, this guide provides clear rationales and is updated to reflect
the latest guidelines. It is an indispensable resource for students aiming to excel in the WGU C959
final exam.
Key Features:
Logic and propositional equivalences
Set theory and operations
Functions, sequences, and summations
Algorithms and complexity analysis
Graph theory and trees
Mathematical induction and recursion
Updates for 2026:
- Updated to reflect 2026/2027 WGU C959 curriculum changes
- Revised answer rationales for clarity and accuracy
- Added new practice questions based on recent exam patterns
- Enhanced explanations for complex topics like graph theory
- Aligned with latest WGU assessment objectives
Abstract:
This study guide is an authoritative resource for students preparing for the WGU C959 Discrete Mathematics I
examination. It consolidates 200 verified questions and solutions, meticulously organized to mirror the exam's
structure and content. The guide covers fundamental discrete mathematics concepts, including logic, set theory,
functions, algorithms, and graph theory, with a focus on application and problem-solving. Each question is
accompanied by a detailed rationale, explaining the correct answer and common misconceptions. The content is
updated to align with the 2026/2027 academic year, ensuring relevance and accuracy. This guide is designed to
facilitate deep understanding and retention, making it an essential tool for achieving a high score. It also includes
strategic tips for tackling exam questions and managing time effectively. By using this guide, students can
confidently approach the exam, knowing they have mastered the core material.
Keywords:
Discrete Mathematics, WGU C959, Exam Study Guide, Logic and Proofs, Set Theory, Graph Theory, Algorithms,
Verified Solutions
Answer Format:
Each question is presented in a multiple-choice format, followed by the correct answer and a comprehensive
rationale. The rationale explains why the correct answer is right and why the distractors are incorrect, reinforcing
key concepts. This format aids in understanding the underlying principles and improves retention.
Compliance Checklist:
All questions are verified against WGU C959 course objectives
Solutions are accurate and aligned with latest academic standards
Page 1
, Content is updated for the 2026/2027 academic year
Rationales are clear and pedagogically sound
Format matches the official exam style
Content Area Overview:
Content Area Questions Key Topics Weight
Logic and Proofs 1-30 Propositional logic, truth tables, logical 15%
equivalences, predicates, quantifiers, proof
techniques
Set Theory 31-60 Sets, subsets, operations, Venn diagrams, 15%
cardinality, power sets, Cartesian products
Functions, Sequences, and 61-90 Functions, injective/surjective/bijective, 15%
Summations composition, inverse, sequences,
summations, growth of functions
Algorithms and Complexity 91-120 Algorithm definition, searching/sorting, 15%
Big-O notation, complexity classes,
recursion
Graph Theory and Trees 121-160 Graph models, terminology, connectivity, 20%
Euler/Hamilton paths, planar graphs, trees,
spanning trees
Induction and Recursion 161-200 Mathematical induction, strong induction, 20%
recursive definitions, recursive algorithms,
structural induction
Page 2
,Q1. Which of the following sets is equinumerous with the power set of the set of
natural numbers?
A. The set of all finite subsets of the natural numbers
B. The set of all functions from the natural numbers to {0,1}
C. The set of all rational numbers
D. The set of all finite sequences of natural numbers
Correct Answer: B. The set of all functions from the natural numbers to {0,1}
Rationale: The power set of the natural numbers has cardinality 2^!50, which is
uncountable. The set of all functions from to {0,1} also has cardinality 2^0, as each
function corresponds to a subset via its indicator function. The other options are all
countable sets.
Why Wrong:
A - The set of finite subsets of is countable, not uncountable.
C - The rationals are countable, so they cannot be equinumerous with the power set of
.
D - The set of finite sequences of natural numbers is countable.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 2.5
Q2. Consider the logical statement: (p -> q) (q -> r). Which of the following is
logically equivalent to its negation?
A. p ¬q r
B. ¬p q ¬r
C. (p ¬q) (q ¬r)
D. ¬(p -> q) ¬(q -> r)
Correct Answer: D. ¬(p -> q) ¬(q -> r)
Rationale: By De Morgan's law, the negation of a conjunction is the disjunction of the
negations. Thus ¬[(p -> q) (q -> r)] ¬(p -> q) ¬(q -> r). Option C is equivalent to the
same because ¬(p -> q) p ¬q and ¬(q -> r) q ¬r, but D is the direct application.
Why Wrong:
A - This represents a specific case, not the full negation.
B - This is not logically equivalent to the negation.
C - This is logically equivalent but not the direct negation form; D is the correct direct
form.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 1.3
Q3. Which of the following relations on the set of integers is an equivalence relation?
A. R = {(a,b) | a + b is even}
B. R = {(a,b) | a - b is odd}
C. R = {(a,b) | a b}
Page 3
, D. R = {(a,b) | a divides b}
Correct Answer: A. R = {(a,b) | a + b is even}
Rationale: The relation 'a + b is even' is reflexive (a+a is even), symmetric (a+b = b+a),
and transitive (if a+b even and b+c even, then a and c have same parity as b, so a+c
even). The others fail transitivity or symmetry.
Why Wrong:
B - This relation is not reflexive because a - a = 0 is even, not odd.
C - This relation is not symmetric (e.g., 1 2 but 2 1 is false).
D - This relation is not symmetric (e.g., 2 divides 4 but 4 does not divide 2).
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 9.5
Q4. How many onto functions are there from a set with 5 elements to a set with 3
elements?
A. 150
B. 243
C. 60
D. 90
Correct Answer: A. 150
Rationale: The number of onto functions from an m-element set to an n-element set is n! *
S(m,n), where S(m,n) is a Stirling number of the second kind. For m=5, n=3, S(5,3)=25, so
3! * 25 = 6 * 25 = 150. Alternatively, inclusion-exclusion: 3^5 - C(3,1)*2^5 + C(3,2)*1^5
= 243 - 96 + 3 = 150.
Why Wrong:
B - 243 is the total number of functions from a 5-element set to a 3-element set (3^5),
not onto.
C - 60 might result from miscounting or using permutations only.
D - 90 is not the correct count; it might come from an incorrect inclusion-exclusion
calculation.
Reference: Rosen, Discrete Mathematics and Its Applications, 8th Ed., Sec. 6.1
Q5. Which of the following statements is true about the sequence defined by a_n =
3a_{n-1} - 2a_{n-2} with a_0 = 2 and a_1 = 3?
A. The sequence is eventually periodic with period 2.
B. The closed form is a_n = 1 + 2^n.
C. The sequence grows exponentially with base 3.
D. The sequence satisfies a_n = 2^n + 1 for all n 0.
Correct Answer: D. The sequence satisfies a_n = 2^n + 1 for all n 0.
Page 4
