Wgu C959 Discrete Math I Exam Comprehensive Questions And Correct Answers Latest Edition 2026

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WGU C959 DISCRETE MATH I EXAM COMPREHENSIVE QUESTIONS AND

CORRECT ANSWERS LATEST EDITION 2026




WGU C959 DISCRETE MATH I

COMPLETE EXAM STUDY GUIDE — QUESTIONS WITH RATIONALES




SECTION 1: PROPOSITIONAL LOGIC

Questions 1–35

1. Which of the following is a proposition?

A) "What time is it?"
B) "Please close the door."
C) "The sky is blue."
D) "This statement is false."

Correct Answer: C
Rationale: A proposition is a declarative statement that is either true or false. "The sky is blue"
has a definite truth value. Questions, commands, and paradoxes are not propositions.




2. Which connective represents "if and only if" in propositional logic?

A) p → q
B) p ∧ q

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C) p ∨ q
D) p ↔ q

Correct Answer: D
Rationale: The biconditional (↔) represents "if and only if" (iff). It is true when both p and q
have the same truth value.




3. The conditional statement p → q is false only when:

A) p is true and q is true
B) p is true and q is false
C) p is false and q is true
D) p is false and q is false

Correct Answer: B
Rationale: The conditional p → q is false only when the hypothesis (p) is true and the conclusion
(q) is false. In all other cases, the conditional is true.



4. Which of the following is a tautology?

A) p ∧ ¬p
B) p ∨ ¬p
C) p → p
D) Both B and C

Correct Answer: D
Rationale: A tautology is a proposition that is always true regardless of the truth values of its
components. Both p ∨ ¬p (Law of Excluded Middle) and p → p are always true. p ∧ ¬p is a
contradiction (always false).




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5. Which of the following is a contradiction?

A) p ∨ ¬p
B) p ∧ ¬p
C) p → p
D) p ∨ p

Correct Answer: B
Rationale: A contradiction is a proposition that is always false regardless of the truth values of
its components. p ∧ ¬p is always false because a proposition cannot be both true and false
simultaneously.




6. What is the converse of the conditional statement "If a number is divisible by 10, then it is
divisible by 5"?

A) If a number is divisible by 5, then it is divisible by 10
B) If a number is not divisible by 10, then it is not divisible by 5
C) If a number is divisible by 10, then it is divisible by 5
D) If a number is not divisible by 5, then it is not divisible by 10

Correct Answer: A
Rationale: The converse of p → q is q → p. So the converse of "If divisible by 10, then divisible
by 5" is "If divisible by 5, then divisible by 10".



7. What is the contrapositive of the conditional statement "If it rains, then the ground is
wet"?

A) If the ground is wet, then it rains
B) If it does not rain, then the ground is not wet
C) If the ground is not wet, then it does not rain
D) If it rains, then the ground is not wet

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Correct Answer: C
Rationale: The contrapositive of p → q is ¬q → ¬p. So the contrapositive of "If it rains, then the
ground is wet" is "If the ground is not wet, then it does not rain." A conditional and its
contrapositive are logically equivalent.




8. What is the inverse of the conditional statement "If you study, then you will pass"?

A) If you pass, then you studied
B) If you do not study, then you will not pass
C) If you do not pass, then you did not study
D) If you study, then you will not pass

Correct Answer: B
Rationale: The inverse of p → q is ¬p → ¬q. So the inverse of "If you study, then you will pass" is
"If you do not study, then you will not pass."



9. Which of the following is logically equivalent to p → q?

A) p ∧ q
B) ¬p ∨ q
C) ¬p ∧ q
D) p ∨ ¬q

Correct Answer: B
Rationale: The conditional p → q is logically equivalent to ¬p ∨ q (Material Implication). This
equivalence is fundamental in propositional logic.



10. According to De Morgan's laws, ¬(p ∧ q) is equivalent to:




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