1
WGU C959 Discrete Math I Exam Study Guide 2025/2026
Complete Questions 1-200 with Verified Solutions & Rationales
Guaranteed Success | Latest Update | Graded A+
SECTION 1: LOGIC & PROOFS (Questions 1-40)
QUESTION 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.
Solution: A proposition is a declarative statement that is either true or false. "The sky is
blue" is a proposition. Questions, commands, and paradoxes are not propositions .
QUESTION 2
Which connective represents "if and only if" in propositional logic?
A) p → q
B) p ∧ q
Sure pass
,2
C) p ∨ q
D) p ↔ q
Solution: The biconditional (↔) represents "if and only if" (iff). It is true when both p and q
have the same truth value .
QUESTION 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
Solution: The implication p → q is false ONLY when the hypothesis (p) is true and the
conclusion (q) is false. This is known as the "vacuously true" exception .
QUESTION 4
What is the converse of the 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 did not rain.
D) If it rains, then the ground is not wet.
Sure pass
,3
Solution: The converse of p → q is q → p. Thus the converse of "If it rains, then the ground
is wet" is "If the ground is wet, then it rains" .
QUESTION 5
What is the contrapositive of the statement "If it rains, then the ground is wet"?
A) If the ground is wet, then it rains.
B) If the ground is not wet, then it did not rain.
C) If it does not rain, then the ground is not wet.
D) If it rains, then the ground is not wet.
Solution: The contrapositive of p → q is ¬q → ¬p. Thus the contrapositive is "If the ground
is not wet, then it did not rain." A conditional statement is logically equivalent to its
contrapositive .
QUESTION 6
Which logical statement is equivalent to ¬(p ∧ q)?
A) ¬p ∧ ¬q
B) ¬p ∨ q
C) ¬p ∨ ¬q
D) p ∨ ¬q
Solution: De Morgan's Law: ¬(p ∧ q) ≡ ¬p ∨ ¬q. Negation of a conjunction is the
disjunction of negations .
Sure pass
, 4
QUESTION 7
Which logical statement is equivalent to ¬(p ∨ q)?
A) ¬p ∨ ¬q
B) ¬p ∧ ¬q
C) ¬p ∨ q
D) p ∧ ¬q
Solution: De Morgan's Law: ¬(p ∨ q) ≡ ¬p ∧ ¬q. Negation of a disjunction is the
conjunction of negations .
QUESTION 8
What is the truth table value of p ∨ ¬p?
A) Always true
B) Always false
C) True when p is true
D) True when p is false
Solution: p ∨ ¬p is a tautology (law of excluded middle). It is always true regardless of the
truth value of p .
QUESTION 9
Sure pass
WGU C959 Discrete Math I Exam Study Guide 2025/2026
Complete Questions 1-200 with Verified Solutions & Rationales
Guaranteed Success | Latest Update | Graded A+
SECTION 1: LOGIC & PROOFS (Questions 1-40)
QUESTION 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.
Solution: A proposition is a declarative statement that is either true or false. "The sky is
blue" is a proposition. Questions, commands, and paradoxes are not propositions .
QUESTION 2
Which connective represents "if and only if" in propositional logic?
A) p → q
B) p ∧ q
Sure pass
,2
C) p ∨ q
D) p ↔ q
Solution: The biconditional (↔) represents "if and only if" (iff). It is true when both p and q
have the same truth value .
QUESTION 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
Solution: The implication p → q is false ONLY when the hypothesis (p) is true and the
conclusion (q) is false. This is known as the "vacuously true" exception .
QUESTION 4
What is the converse of the 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 did not rain.
D) If it rains, then the ground is not wet.
Sure pass
,3
Solution: The converse of p → q is q → p. Thus the converse of "If it rains, then the ground
is wet" is "If the ground is wet, then it rains" .
QUESTION 5
What is the contrapositive of the statement "If it rains, then the ground is wet"?
A) If the ground is wet, then it rains.
B) If the ground is not wet, then it did not rain.
C) If it does not rain, then the ground is not wet.
D) If it rains, then the ground is not wet.
Solution: The contrapositive of p → q is ¬q → ¬p. Thus the contrapositive is "If the ground
is not wet, then it did not rain." A conditional statement is logically equivalent to its
contrapositive .
QUESTION 6
Which logical statement is equivalent to ¬(p ∧ q)?
A) ¬p ∧ ¬q
B) ¬p ∨ q
C) ¬p ∨ ¬q
D) p ∨ ¬q
Solution: De Morgan's Law: ¬(p ∧ q) ≡ ¬p ∨ ¬q. Negation of a conjunction is the
disjunction of negations .
Sure pass
, 4
QUESTION 7
Which logical statement is equivalent to ¬(p ∨ q)?
A) ¬p ∨ ¬q
B) ¬p ∧ ¬q
C) ¬p ∨ q
D) p ∧ ¬q
Solution: De Morgan's Law: ¬(p ∨ q) ≡ ¬p ∧ ¬q. Negation of a disjunction is the
conjunction of negations .
QUESTION 8
What is the truth table value of p ∨ ¬p?
A) Always true
B) Always false
C) True when p is true
D) True when p is false
Solution: p ∨ ¬p is a tautology (law of excluded middle). It is always true regardless of the
truth value of p .
QUESTION 9
Sure pass
