COS3761 LATEST EXAM QUESTIONS
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026
Q&A | INSTANT DOWNLOAD PDF
Core Domains
• Propositional Logic: Syntax, Semantics, and Truth Tables
• Natural Deduction: Proof Systems and Rules of Inference
• Predicate Logic: First-Order Languages, Terms, and Well-Formed
Formulas
• Modal Logic: Kripke Semantics and Possible Worlds
• Logical Validity, Satisfiability, and Model Theory
• Translation between Natural Language and Formal Logic
• Advanced Proof Techniques: Sequent Calculus and Derivations
Introduction
This examination assesses comprehensive knowledge and applied skills in
formal logic, encompassing propositional and predicate logic, natural
deduction systems, modal logic with Kripke semantics, and advanced
proof techniques. Candidates are expected to demonstrate proficiency in
translating natural language statements into formal languages, evaluating
validity and satisfiability, constructing rigorous proofs using introduction
and elimination rules, and reasoning about logical systems within
computational and philosophical contexts. The examination consists of
multiple-choice questions and scenario-based problems designed to test
,both foundational understanding and higher-order critical thinking. Each
question requires careful analysis, application of logical principles, and
clinical decision-making within the framework of formal reasoning.
Success on this examination reflects mastery of the core competencies
required for advanced study in logic, computer science, and related
disciplines.
SECTION ONE: QUESTIONS 1–100
Question 1
Which of the following is a well-formed formula (wff) in propositional
logic?
A. (P ∧ Q) → R
B. P ∧ → Q
C. (P ∨ Q
D. P → ∧ Q
A. (P ∧ Q) → R
RATIONALE: A well-formed formula in propositional logic must
follow strict syntactic rules. Option A is correctly formed with
parentheses around the conjunction and the conditional connective
properly placed. Options B, C, and D violate syntax rules due to missing
operands or mismatched parentheses.
Question 2
In predicate logic, which of the following is a term?
A. P(x)
B. f(a, b)
,C. ∀x P(x)
D. P(x) → Q(y)
B. f(a, b)
RATIONALE: In predicate logic, terms are expressions that denote
objects. They include constants (a, b), variables (x, y), and function
symbols applied to terms (f(a, b)). Predicates (P(x)) and formulas with
quantifiers (∀x P(x)) are not terms.
Question 3
The formula ¬(P ∧ Q) is logically equivalent to:
A. ¬P ∧ ¬Q
B. ¬P ∨ ¬Q
C. P ∨ Q
D. P → ¬Q
B. ¬P ∨ ¬Q
RATIONALE: By De Morgan's law, the negation of a conjunction is
equivalent to the disjunction of the negations. ¬(P ∧ Q) ≡ ¬P ∨ ¬Q. This
is a fundamental equivalence in classical logic.
Question 4
Which rule of inference allows one to infer Q from P → Q and P?
A. Modus tollens
B. Modus ponens
C. Hypothetical syllogism
D. Disjunctive syllogism
B. Modus ponens
, RATIONALE: Modus ponens (also known as implication elimination)
states that if P → Q is true and P is true, then Q can be inferred. This is
one of the most fundamental rules of inference in natural deduction.
Question 5
In a Kripke model for modal logic, the truth of □φ at a world w depends
on:
A. The truth of φ at w only
B. The truth of φ at all worlds accessible from w
C. The truth of φ at some world accessible from w
D. The truth of φ at the actual world only
B. The truth of φ at all worlds accessible from w
RATIONALE: In Kripke semantics, the necessity operator □ means "in
all accessible possible worlds." □φ is true at world w if and only if φ is
true at every world v such that wRv (w accesses v).
Question 6
Translate the following English sentence into propositional logic: "The
house is used as a guesthouse only if it has seven bathrooms." Let S =
"The house is used as a guesthouse" and R = "The house has seven
bathrooms."
A. S → R
B. R → S
C. S ↔ R
D. ¬S → ¬R
A. S → R
RATIONALE: The phrase "only if" introduces a necessary condition.
"S only if R" means that S cannot occur without R, which is logically
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026
Q&A | INSTANT DOWNLOAD PDF
Core Domains
• Propositional Logic: Syntax, Semantics, and Truth Tables
• Natural Deduction: Proof Systems and Rules of Inference
• Predicate Logic: First-Order Languages, Terms, and Well-Formed
Formulas
• Modal Logic: Kripke Semantics and Possible Worlds
• Logical Validity, Satisfiability, and Model Theory
• Translation between Natural Language and Formal Logic
• Advanced Proof Techniques: Sequent Calculus and Derivations
Introduction
This examination assesses comprehensive knowledge and applied skills in
formal logic, encompassing propositional and predicate logic, natural
deduction systems, modal logic with Kripke semantics, and advanced
proof techniques. Candidates are expected to demonstrate proficiency in
translating natural language statements into formal languages, evaluating
validity and satisfiability, constructing rigorous proofs using introduction
and elimination rules, and reasoning about logical systems within
computational and philosophical contexts. The examination consists of
multiple-choice questions and scenario-based problems designed to test
,both foundational understanding and higher-order critical thinking. Each
question requires careful analysis, application of logical principles, and
clinical decision-making within the framework of formal reasoning.
Success on this examination reflects mastery of the core competencies
required for advanced study in logic, computer science, and related
disciplines.
SECTION ONE: QUESTIONS 1–100
Question 1
Which of the following is a well-formed formula (wff) in propositional
logic?
A. (P ∧ Q) → R
B. P ∧ → Q
C. (P ∨ Q
D. P → ∧ Q
A. (P ∧ Q) → R
RATIONALE: A well-formed formula in propositional logic must
follow strict syntactic rules. Option A is correctly formed with
parentheses around the conjunction and the conditional connective
properly placed. Options B, C, and D violate syntax rules due to missing
operands or mismatched parentheses.
Question 2
In predicate logic, which of the following is a term?
A. P(x)
B. f(a, b)
,C. ∀x P(x)
D. P(x) → Q(y)
B. f(a, b)
RATIONALE: In predicate logic, terms are expressions that denote
objects. They include constants (a, b), variables (x, y), and function
symbols applied to terms (f(a, b)). Predicates (P(x)) and formulas with
quantifiers (∀x P(x)) are not terms.
Question 3
The formula ¬(P ∧ Q) is logically equivalent to:
A. ¬P ∧ ¬Q
B. ¬P ∨ ¬Q
C. P ∨ Q
D. P → ¬Q
B. ¬P ∨ ¬Q
RATIONALE: By De Morgan's law, the negation of a conjunction is
equivalent to the disjunction of the negations. ¬(P ∧ Q) ≡ ¬P ∨ ¬Q. This
is a fundamental equivalence in classical logic.
Question 4
Which rule of inference allows one to infer Q from P → Q and P?
A. Modus tollens
B. Modus ponens
C. Hypothetical syllogism
D. Disjunctive syllogism
B. Modus ponens
, RATIONALE: Modus ponens (also known as implication elimination)
states that if P → Q is true and P is true, then Q can be inferred. This is
one of the most fundamental rules of inference in natural deduction.
Question 5
In a Kripke model for modal logic, the truth of □φ at a world w depends
on:
A. The truth of φ at w only
B. The truth of φ at all worlds accessible from w
C. The truth of φ at some world accessible from w
D. The truth of φ at the actual world only
B. The truth of φ at all worlds accessible from w
RATIONALE: In Kripke semantics, the necessity operator □ means "in
all accessible possible worlds." □φ is true at world w if and only if φ is
true at every world v such that wRv (w accesses v).
Question 6
Translate the following English sentence into propositional logic: "The
house is used as a guesthouse only if it has seven bathrooms." Let S =
"The house is used as a guesthouse" and R = "The house has seven
bathrooms."
A. S → R
B. R → S
C. S ↔ R
D. ¬S → ¬R
A. S → R
RATIONALE: The phrase "only if" introduces a necessary condition.
"S only if R" means that S cannot occur without R, which is logically
