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WGU C959 Discrete Math I Exam Study Guide
2026/2027
Complete Questions with Verified Solutions & Rationales
Guaranteed Success | Latest Update | Graded A+
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 .
QUESTION 4
What is the converse of the statement "If it rains, then the ground is wet"?
Sure pass
,3
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.
Solution: The converse of p → q is q → p. Thus the converse 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. A conditional statement is
logically equivalent to its contrapositive .
QUESTION 6
Sure pass
, 4
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 .
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 .
Sure pass
WGU C959 Discrete Math I Exam Study Guide
2026/2027
Complete Questions with Verified Solutions & Rationales
Guaranteed Success | Latest Update | Graded A+
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 .
QUESTION 4
What is the converse of the statement "If it rains, then the ground is wet"?
Sure pass
,3
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.
Solution: The converse of p → q is q → p. Thus the converse 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. A conditional statement is
logically equivalent to its contrapositive .
QUESTION 6
Sure pass
, 4
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 .
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 .
Sure pass
