Texas A&M University (TAMU) PHIL 240 Introduction to Logic Exam 1 Practice

These questions are part of the practice quiz. Start practicing

• From ∀x (P(x) → ∃y Q(x,y)) can we move ∃y outside?
• Which translation represents 'All humans are mortal' in predicate logic?
• Which statement correctly expresses Modus Tollens?
• Which statement best describes an argument?
• Given ∀x (P(x) → Q) and ∃x P(x), which of the following is guaranteed?
• Compound Sentence?
• Which is the correct general rule for discharging assumptions inside nested scopes?
• What is the contrapositive of p → q?
• What is the English translation for a biconditional?
• Which translation correctly renders 'Some student passed'?
• Translate: 'Every student who takes a course loves the course.'
• Sentential/Propositional Logic is the simplest level of logical structure and analyzes how complete sentences are combined using which connectives?
• Which of the following is a valid conditional exchange for p -> q?
• Which of the following is a contradiction?
• In logic, which concept is defined as the relationship where the premises guarantee the conclusion?
• Which statement is a valid reading of the universal instantiation rule?
• Which replacement rule allows swapping the order of parts of a conjunction?
• The contrapositive of p → q is what?
• Which inference is valid from a conjunction A and B?
• Are ∀x ∃y P(x,y) and ∃y ∀x P(x,y) equivalent?
• Statement Variable
• Conjunction Introduction: From p and q, infer?
• Negate ∀x ∃y P(x,y). Which of the following is equivalent?
• Which statement best describes Indirect Proof (IP)?
• Which translation represents 'Some student passed'?
• Which of the following statements is true about existential instantiation (EI)?
• What is the English translation for a disjunction?
• What does Commutation permit?
• Statement Form
• Which is satisfiable but not valid?
• What does entailment mean in logic?
• Which best captures the nature of logic?
• What is a counterexample to an argument form?
• Which statement correctly defines a valid deductive argument form?
• Which option best describes the main goal of logic as a field of study?
• From P(c) infer ∃x P(x). What rule is this?
• Replacement rules can be applied to which parts of a formula?
• Sentential Operator
• To derive ∀x P(x) from P(a) when a is arbitrary, what condition must hold?
• Which is a valid application of Modus Ponens?
• A derivation is best described as what?
• What is the contrapositive of the conditional p -> q?
• Absorption law: p ∨ (p ∧ q) simplifies to which?
• The biconditional p <-> q is logically equivalent to which of the following?
• Double negation is equivalent to which of the following?
• Conditional (definition) states that a formula asserts what?
• Is p ∧ ¬p satisfiable?
• Which of the following is an example of Double Negation?
• Which statement about quantifier order is correct?
• Reductio ad absurdum: What justifies deriving p from a contradiction of ¬p?
• Is (p ∨ ¬p) a tautology?
• Provide a counterexample to show that ∀x ∃y P(x,y) does not imply ∃y ∀x P(x,y).
• If p → q and q → r, what can we conclude?
• Which statement correctly expresses De Morgan's laws?
• Given two conditionals and the disjunction of the antecedents, what is inferred?
• What is the constructive-dilemma form?
• Which form of statement is proven without any premises?
• Duplication rule for identical components: If in a disjunction or conjunction the two parts are the same, the expression is equivalent to?
• Conjunction Elimination: From p ∧ q, infer?
• A derivation is best described as what?
• Indirect proofs are used to prove what?
• Logic is a normative enterprise; what does this imply about its aims?
• From A and B, which conclusion is valid?
• In a complex logical expression, which determines the overall sentence type?
• Which statements characterize one-variable predicate logic?
• What are the two sorts of arguments for deductive reasoning?
• Which statement is logically equivalent to p → q?
• The standard equivalence for p → q is which disjunction?
• Which of the following describes Modus Ponens?
• What is the validity status of the form 'Affirming the consequent'?
• Which of the following statements would most accurately reflect a central concern of logic?
• Which statement best describes Conditional Proof (CP)?
• In an inductive argument, the premises provide what degree of support for the conclusion?
• Apply De Morgan's law to ¬(p ∧ q).
• Which of the following is a tautology?
• Which option illustrates Denying the Antecedent?
• Which of the following best captures a core activity of logic?
• In the conditional statement 'If Caesar conquered Gaul, he was a great general,' which part is the antecedent?
• With respect to rules of formation, what must be true for a disjunction to be part of a well-formed formula?
• In De Morgan's laws, Not (P and Q) is equivalent to?
• Statement Constant
• Which statement correctly describes a sentential operator's role?
• True or false: (p → q) ∨ (q → p) is a tautology.
• Which formula expresses 'There exist at least two distinct individuals with P'?
• Which replacement rule expresses moving a conditional across a conjunction?
• P <-> Q is logically equivalent to which conjunction?
• What is the validity status of the form 'Denying the antecedent'?
• In a proof, the final step must be the conclusion.
• The contrapositive of p → q is which of the following?
• Which of the following best exemplifies a core concern of logic?
• Which rule allows deriving P → R from P → Q and Q → R?
• Which of the following is a Rule of Inference?
• Indicate the expected outcome of an Indirect Proof when assuming p and deriving a contradiction.
• What is a Theorem in this context?
• Which is valid?
• What is the role of formal methods in logic?
• Which statement describes a contradiction?
• Which statement best describes a disjunction?
• What is the English translation for a conditional?
• What is the equivalent of ¬¬p?
• Absorption laws: p ∨ (p ∧ q) simplifies to what?
• Are ∀x ∃y P(x,y) and ∃y ∀x P(x,y) equivalent in general?
• Which statement best illustrates Hypothetical Syllogism?
• In the same conditional, which part is the consequent?
• Which option best presents the biconditional for 'You will pass if and only if you study'?
• What is the main aim of logic as described in the course overview?
• Which rule justifies deriving P(a) from ∀x P(x) for an arbitrary constant a?
• Conditional proofs are used to prove what?
• Which statement expresses the Hypothetical Syllogism?
• Which statement describes Double Negation (DN)?
• Which formula expresses 'There exists an x such that P(x) and not Q(x)'?
• Which of the following defines a sound argument?
• What determines whether a logical argument is valid?
• Which rule justifies deriving q from p ∨ q and ¬p?
• Which statement best describes deduction?
• From p -> q and not q, which conclusion is warranted by Modus Tollens?
• Which is the contrapositive of the conditional P -> Q?
• The negation of ∃x P(x) is equivalent to what?
• If p is true and q is false, then p ∧ q is ...
• When discharging nested assumptions, in which order should they be discharged?
• Determine the truth value of (p ∧ q) → r when p = True, q = False, r = True.
• Which of the following statements captures the aim of logic?
• Which is the correct translation of 'There exists x such that if x is a student then x loves x'?
• From p ∧ q, which of the following is a valid direct inference?
• Is (p ∧ q) ↔ (q ∧ p) a tautology?
• Use distributive law to simplify p ∨ (q ∧ r).
• Which of the following is Modus Ponens?
• What does a Biconditional express?
• Which option best describes the scope of logic in evaluating arguments?
• Which best defines a proof?
• What syntactical element do well-formed formulas require?
• Which formula is valid (and hence satisfiable)?
• What best defines an argument in logic?
• Which of the following is a Replacement Rule?
• The negation of ∀x P(x) is equivalent to what?
• If p → q is true and p is false, what can be concluded about q?
• Which formula is satisfiable but not valid?
• From p ∨ q and ¬p, what can we conclude?
• Is 'If p then q' a compound sentence?
• What does Association state about grouping of conjuncts and disjuncts?
• Which statement about validity and entailment is accurate?
• De Morgan's law for ¬(p ∨ q) is equivalent to
• Is p → q logically equivalent to ¬p ∨ q?
• Double negation elimination: Not Not P can be replaced by P. Which option states this correctly?
• In a deductive argument, the premises are intended to provide what?
• Which expression correctly represents 'It is not the case that every student passed'?
• When applying existential generalization, which condition is necessary?
• Which inference is valid by Modus Ponens?
• Which formula expresses there are two different objects that both satisfy P?
• There exist at least two tall.
• Which expression is equivalent to the negation of ∃x P(x)?
• Which statement reflects a central methodological concern of logic?
• Which rule justifies inferring ∃x P(x) from P(c) when c is a new constant not appearing in undischarged assumptions?
• If P or Q is true, and not P, what can we conclude?
• What is the English translation for negation (tilde)?
• Exportation states that (P ∧ Q) -> R is equivalent to which form?
• In the conditional sentence 'If it rains, the picnic will be canceled', which part is the antecedent?
• Which statement is an equivalent form of 'No dogs are cats'?
• Which option correctly describes the difference between deductive and inductive arguments?
• What is the negation of the statement 'All humans are mortal'?
• Which description best captures a basic topic studied in logic?
• Provide a valid formula.
• Which statement best describes a Justified Step?
• Which expression correctly represents 'There is no student who passed'?
• Which statement best contrasts statement constants and statement variables?
• What is the English translation for the logical conjunction symbol?
• Translate: There exists at least two tall.
• Which formalization expresses 'No dogs are cats'?
• Logic aims to provide a rigorous framework for assessing arguments. Which phrase best captures this aim?
• From a statement P, which of the following can be inferred?
• Which statement best captures the directional nature of Replacement Rules?
• What does Duplication mean when both disjuncts or conjuncts are the same?
• Which statement is a characteristic of Replacement Rules?
• Are ∀x ∀y P(x,y) and ∀y ∀x P(x,y) equivalent?
• Which formula is a tautology?
• Exportation states that if p and q then r is equivalent to which of the following?
• Which feature best distinguishes a statement variable from a statement constant?
• Which formula expresses the distribution of conjunction over disjunction?
• Which formula contains a free variable?
• From ∃x P(x) infer P(c) for some new constant c. What rule is this?