Virtual Labs

Propositional Logic: Syntax and Inference

All logical sentences can be written using only:

a: ∧ and ∨ Explanation

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b: ¬, ∧ and ∨ Explanation

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c: ⇒ and ¬ Explanation

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d: None of the above. Explanation

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Which of the following is equivalent to p → q?

a: ¬p ∨ q Explanation

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b: p ∧ q Explanation

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c: ¬p ∧ q Explanation

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d: p ∨ ¬q Explanation

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What is the negation of 'p ∧ q'?

a: ¬p ∧ ¬q Explanation

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b: ¬p ∨ ¬q Explanation

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c: ¬(p ∨ q) Explanation

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d: p ∨ q Explanation

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Which of the following rules allows us to conclude q from premises p → q and ¬p → q?

a: Modus Ponens Explanation

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b: Modus Tollens Explanation

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c: Case Analysis Explanation

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d: Hypothetical Syllogism Explanation

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What is the minimal number of rows needed in a truth table to prove that two propositional formulas with 3 variables are NOT equivalent?

a: 1 Explanation

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b: 4 Explanation

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c: 8 Explanation

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d: 16 Explanation

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Given the premises 'If it rains, the ground is wet' and 'The ground is not wet', what can be validly concluded?

a: It must be raining Explanation

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b: It might be raining Explanation

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c: It is not raining Explanation

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d: We cannot conclude anything about rain Explanation

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Which of the following is a valid step in converting a formula to Conjunctive Normal Form (CNF)?

a: Replace p → q with p ∧ ¬q Explanation

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b: Replace p → q with ¬p ∨ q Explanation

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c: Replace ¬(p ∨ q) with ¬p ∨ ¬q Explanation

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d: Replace p ↔ q with (p → q) ∨ (q → p) Explanation

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In propositional logic, which of the following best describes a sound argument?

a: An argument where the conclusion follows from the premises using valid rules Explanation

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b: An argument with true premises and a true conclusion Explanation

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c: An argument that is valid and has true premises Explanation

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d: An argument where each step uses only one inference rule Explanation

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Which logical law is being applied in the following equivalence: ¬(p → q) ≡ p ∧ ¬q?

a: De Morgan's Laws Explanation

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b: Distributive Law Explanation

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c: Double Negation Law Explanation

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d: Material Implication Explanation

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