Logic And Critical Thinking Practice Exam

Question 1 Logic And Critical Thinking

What is a valid argument?

The contrapositive of P → Q is ¬Q → ¬P. A conditional and its contrapositive are logically equivalent. All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises. Negation (¬P) reverses the truth value of a proposition: if P is true, ¬P is false, and vice versa. A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth.

Question 2 Logic And Critical Thinking

What is the base rate fallacy?

Every object is identical to itself. In propositional logic: P ≡ P. A thing is what it is. Ignoring the general prevalence (base rate) of an event when evaluating probability, and focusing instead on specific but less informative evidence. ¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q). Negating a conjunction gives a disjunction of negations, and vice versa. The obligation falls on the person making a claim to provide evidence, rather than on others to disprove it.

Question 3 Logic And Critical Thinking

What is a truth table?

A truth table is a mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its components. The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings. Abductive reasoning (inference to the best explanation) starts with observations and seeks the simplest, most likely explanation. Example: wet streets → it probably rained. Assuming the truth must be a compromise between two opposing positions, regardless of the evidence for each side.

Question 4 Logic And Critical Thinking

What is the equivocation fallacy?

Using an ambiguous term in more than one sense within an argument, leading to a misleading conclusion. The default assumption that there is no effect or no relationship between variables. Experiments aim to gather evidence to reject or fail to reject it. Claiming something is true because an authority figure says so, especially when the authority is not an expert in the relevant field or when experts disagree. ∃x P(x) means "there exists at least one x for which P(x) is true."

Question 5 Logic And Critical Thinking

What is the straw man fallacy?

The straw man fallacy misrepresents someone's argument to make it easier to attack. The arguer refutes a distorted version instead of the actual position. Every object is identical to itself. In propositional logic: P ≡ P. A thing is what it is. Abductive reasoning selects the best explanation for given data, while inductive reasoning generalizes from specific instances to broader rules. A type of ad hominem that deflects criticism by pointing out the opponent's hypocrisy: "You do it too!" It does not address the argument itself.

Question 6 Logic And Critical Thinking

What is the post hoc ergo propter hoc fallacy?

Negation (¬P) reverses the truth value of a proposition: if P is true, ¬P is false, and vice versa. Assuming that because event B followed event A, A caused B. Correlation or sequence does not imply causation. false in all other cases. The converse of P → Q is Q → P. The converse is not logically equivalent to the original conditional.

Question 7 Logic And Critical Thinking

What is hindsight bias?

Negation (¬P) reverses the truth value of a proposition: if P is true, ¬P is false, and vice versa. The tendency to believe, after an event has occurred, that one "knew it all along", making outcomes seem more predictable than they were. Q is true; therefore P is true. This is invalid because Q could be true for reasons other than P. Judging something as good or bad based on where it comes from (its origin) rather than its current merit or evidence.

Question 8 Logic And Critical Thinking

What is a reductio ad absurdum?

Continuing a behavior or endeavor because of previously invested resources (time, money, effort) rather than evaluating current and future value. Arguing that something is true or good because many people believe it or do it. ∀x P(x) means "for all x, P(x) is true." Every element in the domain satisfies the predicate P. A method of argument that assumes a proposition is true and then shows it leads to a contradiction or absurd consequence, thereby proving it false.

Question 9 Logic And Critical Thinking

What is the circular reasoning (begging the question) fallacy?

P is true; therefore Q is true. (P → Q, P ⊢ Q) A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth. An argument where the conclusion is assumed in one of the premises. Example: "The Bible is true because it is the word of God, and we know it is the word of God because the Bible says so." All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Question 10 Logic And Critical Thinking

What is the law of non-contradiction?

A proposition cannot be both true and false at the same time and in the same sense. (¬(P ∧ ¬P)) The tendency for people to react differently depending on how information is presented (framed)—e.g., "90% survival rate" vs. "10% mortality rate." P is false; therefore Q is false. This is invalid because Q might be true independently of P. All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Question 11 Logic And Critical Thinking

What is the loaded question fallacy?

A phenomenon where the desire for group harmony or conformity overrides realistic appraisal of alternatives, leading to poor decision-making. Asking a question that contains a presupposition or assumption that has not been proven. Example: "When did you stop cheating on exams?" Claiming something is true because it hasn't been proven false, or false because it hasn't been proven true. causation means one directly produces the other. Correlation alone does not prove a causal link.

Question 12 Logic And Critical Thinking

What is the tu quoque fallacy?

Rejecting the null hypothesis when it is actually true—concluding there is an effect when there is none. All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises. Presenting only two options as if they are the only possibilities when, in fact, other alternatives exist. A type of ad hominem that deflects criticism by pointing out the opponent's hypocrisy: "You do it too!" It does not address the argument itself.

Question 13 Logic And Critical Thinking

What is logical negation (NOT)?

Negation (¬P) reverses the truth value of a proposition: if P is true, ¬P is false, and vice versa. P is false; therefore Q is false. This is invalid because Q might be true independently of P. Asking a question that contains a presupposition or assumption that has not been proven. Example: "When did you stop cheating on exams?" A biconditional (P ↔ Q) is true when both P and Q have the same truth value (both true or both false).

Question 14 Logic And Critical Thinking

What is formal logic?

The slippery slope fallacy claims that one event will inevitably lead to a chain of extreme consequences without providing evidence for each step in the chain. Formal logic is the study of inference with purely formal content, where the validity of an argument depends solely on its logical form rather than the meaning of its terms. A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth. Drawing a broad conclusion from a small or unrepresentative sample. Example: "I met two rude people from that city, so everyone there must be rude."

Question 15 Logic And Critical Thinking

What is the red herring fallacy?

A type of ad hominem that deflects criticism by pointing out the opponent's hypocrisy: "You do it too!" It does not address the argument itself. An argument with an unstated (implicit) premise that the audience is expected to fill in. Example: "She's a doctor, so she's smart" (implicit: doctors are smart). Introducing an irrelevant topic into a discussion to divert attention from the original issue. If removing one grain from a heap still leaves a heap, when does it stop being a heap? It highlights the problem of vague predicates and unclear boundaries.

Question 16 Logic And Critical Thinking

What is the square of opposition?

Applying standards, rules, or principles to others while exempting oneself or one's case without adequate justification. A method of updating the probability of a hypothesis based on new evidence using Bayes' theorem: P(H|E) = P(E|H) × P(H) / P(E). A diagram showing logical relationships among categorical propositions: contradictory, contrary, subcontrary, and subalternation relations. The ad hominem fallacy attacks the person making the argument rather than the argument itself. Example: "You can't trust John's climate data—he's not even a scientist."

Question 17 Logic And Critical Thinking

What is modus ponens?Modus ponens: If P then Q

A method of updating the probability of a hypothesis based on new evidence using Bayes' theorem: P(H|E) = P(E|H) × P(H) / P(E). Arguing that something is good because it is "natural" or bad because it is "unnatural." Naturalness alone does not determine value or correctness. Occam's razor states that among competing hypotheses, the one with the fewest assumptions should be preferred. "Do not multiply entities beyond necessity." P is true; therefore Q is true. (P → Q, P ⊢ Q)

Question 18 Logic And Critical Thinking

What is a type I error (false positive)?

An argument with an unstated (implicit) premise that the audience is expected to fill in. Example: "She's a doctor, so she's smart" (implicit: doctors are smart). Rejecting the null hypothesis when it is actually true—concluding there is an effect when there is none. Every object is identical to itself. In propositional logic: P ≡ P. A thing is what it is. Ignoring the general prevalence (base rate) of an event when evaluating probability, and focusing instead on specific but less informative evidence.

Question 19 Logic And Critical Thinking

What is the burden of proof in an argument?

The mental discomfort experienced when holding two or more contradictory beliefs, leading people to change beliefs or rationalize to reduce the tension. Arguing that something is true or good because many people believe it or do it. The obligation falls on the person making a claim to provide evidence, rather than on others to disprove it. A deductive argument is either valid or invalid (all-or-nothing). An inductive argument is strong or weak depending on how probable the conclusion is given the premises.

Question 20 Logic And Critical Thinking

What is the paradox of the heap (sorites paradox)?

¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q). Negating a conjunction gives a disjunction of negations, and vice versa. If removing one grain from a heap still leaves a heap, when does it stop being a heap? It highlights the problem of vague predicates and unclear boundaries. A premise is a statement in an argument that provides evidence or reasons for the conclusion. Abductive reasoning (inference to the best explanation) starts with observations and seeks the simplest, most likely explanation. Example: wet streets → it probably rained.

Question 21 Logic And Critical Thinking

What is the division fallacy?

Assuming that what is true of the whole must be true of each part. Example: "The university is prestigious, so every department must be prestigious." Every swan I have observed is white. Therefore, all swans are probably white. The conclusion is probable but not certain. A systematic process: observation → question → hypothesis → experiment → analysis → conclusion, designed to test ideas through repeatable, empirical investigation. Using an ambiguous term in more than one sense within an argument, leading to a misleading conclusion.

Question 22 Logic And Critical Thinking

What is the middle ground (argument to moderation) fallacy?

A non sequitur is an argument in which the conclusion does not logically follow from the premises. A hypothesis is a testable, falsifiable prediction about the relationship between variables, formulated before experimentation. not P; therefore Q. (P ∨ Q, ¬P ⊢ Q) Assuming the truth must be a compromise between two opposing positions, regardless of the evidence for each side.

Question 23 Logic And Critical Thinking

What is the composition fallacy?

An argument where the conclusion is assumed in one of the premises. Example: "The Bible is true because it is the word of God, and we know it is the word of God because the Bible says so." Assuming that what is true of the parts must be true of the whole. Example: "Every player on the team is excellent, so the team must be excellent." Claiming something is true because an authority figure says so, especially when the authority is not an expert in the relevant field or when experts disagree. A tautology is a compound statement that is true for every possible assignment of truth values to its variables (e.g., P ∨ ¬P).

Question 24 Logic And Critical Thinking

What is a non sequitur?

there is no middle ground. (P ∨ ¬P) false only when both are false. The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings. A non sequitur is an argument in which the conclusion does not logically follow from the premises.

Question 25 Logic And Critical Thinking

How does Occam's razor apply to scientific reasoning?

The obligation falls on the person making a claim to provide evidence, rather than on others to disprove it. Occam's razor states that among competing hypotheses, the one with the fewest assumptions should be preferred. "Do not multiply entities beyond necessity." The major term (predicate of conclusion), minor term (subject of conclusion), and middle term (appears in both premises but not the conclusion). It guides scientists to prefer the simplest explanation that accounts for the evidence, reducing the risk of overfitting and unnecessary complexity.

Question 26 Logic And Critical Thinking

What are the three terms in a categorical syllogism?

false only when both are false. The obligation falls on the person making a claim to provide evidence, rather than on others to disprove it. Applying standards, rules, or principles to others while exempting oneself or one's case without adequate justification. The major term (predicate of conclusion), minor term (subject of conclusion), and middle term (appears in both premises but not the conclusion).

Question 27 Logic And Critical Thinking

What does the universal quantifier (∀) mean?

It guides scientists to prefer the simplest explanation that accounts for the evidence, reducing the risk of overfitting and unnecessary complexity. Q is true; therefore P is true. This is invalid because Q could be true for reasons other than P. ∀x P(x) means "for all x, P(x) is true." Every element in the domain satisfies the predicate P. A deductive argument is either valid or invalid (all-or-nothing). An inductive argument is strong or weak depending on how probable the conclusion is given the premises.

Question 28 Logic And Critical Thinking

What is reproducibility in the scientific method?

An informal fallacy is an error in reasoning whose flaw lies in the content, context, or delivery of the argument rather than its logical form. The ad hominem fallacy attacks the person making the argument rather than the argument itself. Example: "You can't trust John's climate data—he's not even a scientist." The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings. Ignoring the general prevalence (base rate) of an event when evaluating probability, and focusing instead on specific but less informative evidence.

Question 29 Logic And Critical Thinking

What is the Dunning-Kruger effect?

The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings. Continuing a behavior or endeavor because of previously invested resources (time, money, effort) rather than evaluating current and future value. Assuming that because event B followed event A, A caused B. Correlation or sequence does not imply causation. A cognitive bias where people with low ability overestimate their competence, while those with high ability may underestimate theirs.

Question 30 Logic And Critical Thinking

What is a self-fulfilling prophecy and how does it relate to reasoning?

A prediction that causes itself to become true because believing it changes behavior. It illustrates how expectations can bias outcomes and compromise objective reasoning. A truth table is a mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its components. A method of argument that assumes a proposition is true and then shows it leads to a contradiction or absurd consequence, thereby proving it false. Abductive reasoning selects the best explanation for given data, while inductive reasoning generalizes from specific instances to broader rules.

Question 31 Logic And Critical Thinking

What is an informal fallacy?

An informal fallacy is an error in reasoning whose flaw lies in the content, context, or delivery of the argument rather than its logical form. If removing one grain from a heap still leaves a heap, when does it stop being a heap? It highlights the problem of vague predicates and unclear boundaries. The straw man fallacy misrepresents someone's argument to make it easier to attack. The arguer refutes a distorted version instead of the actual position. Applying standards, rules, or principles to others while exempting oneself or one's case without adequate justification.

Question 32 Logic And Critical Thinking

What is De Morgan's Law in logic?

When evaluating an argument, interpret it in the strongest, most reasonable form before critiquing it—do not attack a weak version. Formal logic is the study of inference with purely formal content, where the validity of an argument depends solely on its logical form rather than the meaning of its terms. ¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q). Negating a conjunction gives a disjunction of negations, and vice versa. Arguing that something is true or good because many people believe it or do it.

Question 33 Logic And Critical Thinking

What is deductive validity vs. inductive strength?

Assuming that what is true of the parts must be true of the whole. Example: "Every player on the team is excellent, so the team must be excellent." true in all other cases. false only when both are false. A deductive argument is either valid or invalid (all-or-nothing). An inductive argument is strong or weak depending on how probable the conclusion is given the premises.

Question 34 Logic And Critical Thinking

What is a biconditional (IF AND ONLY IF)?

A branch of logic dealing with propositions (statements that are true or false) and logical connectives (AND, OR, NOT, IF…THEN, IF AND ONLY IF). A biconditional (P ↔ Q) is true when both P and Q have the same truth value (both true or both false). A non sequitur is an argument in which the conclusion does not logically follow from the premises. Using an ambiguous term in more than one sense within an argument, leading to a misleading conclusion.

Question 35 Logic And Critical Thinking

What is peer review in science?

∃x P(x) means "there exists at least one x for which P(x) is true." A process where scientific work is evaluated by independent experts in the field before publication, to check methodology, accuracy, and significance. The converse of P → Q is Q → P. The converse is not logically equivalent to the original conditional. Extends propositional logic with quantifiers (∀ for all, ∃ there exists) and predicates to express properties of objects and relations between them.

Question 36 Logic And Critical Thinking

What is anchoring bias?

Abductive reasoning selects the best explanation for given data, while inductive reasoning generalizes from specific instances to broader rules. A phenomenon where the desire for group harmony or conformity overrides realistic appraisal of alternatives, leading to poor decision-making. The tendency to rely too heavily on the first piece of information encountered (the "anchor") when making decisions. Deductive reasoning moves from general premises to a specific, certain conclusion. Inductive reasoning moves from specific observations to a general, probable conclusion.

Question 37 Logic And Critical Thinking

What is an analogy in argumentation?

An analogy argues that because two things are similar in some respects, they are likely similar in some further respect. Strength depends on relevance of similarities. A method of argument that assumes a proposition is true and then shows it leads to a contradiction or absurd consequence, thereby proving it false. The mental discomfort experienced when holding two or more contradictory beliefs, leading people to change beliefs or rationalize to reduce the tension. A biconditional (P ↔ Q) is true when both P and Q have the same truth value (both true or both false).

Question 38 Logic And Critical Thinking

What is the availability heuristic?

there is no middle ground. (P ∨ ¬P) not P; therefore Q. (P ∨ Q, ¬P ⊢ Q) Every object is identical to itself. In propositional logic: P ≡ P. A thing is what it is. Judging the likelihood of events based on how easily examples come to mind, which can overestimate vivid or recent events.

Question 39 Logic And Critical Thinking

What is the Texas sharpshooter fallacy?

Cherry-picking data clusters to suit a hypothesis after the fact—like drawing a target around bullet holes. It ignores the data that doesn't fit. An argument is a set of statements (premises) offered as reasons to support a conclusion. Claiming something is true because it hasn't been proven false, or false because it hasn't been proven true. A tautology is a compound statement that is true for every possible assignment of truth values to its variables (e.g., P ∨ ¬P).

Question 40 Logic And Critical Thinking

What is the no true Scotsman fallacy?

Drawing a broad conclusion from a small or unrepresentative sample. Example: "I met two rude people from that city, so everyone there must be rude." Every swan I have observed is white. Therefore, all swans are probably white. The conclusion is probable but not certain. A type of ad hominem that deflects criticism by pointing out the opponent's hypocrisy: "You do it too!" It does not address the argument itself. Redefining a group to exclude counterexamples rather than accepting them. Example: "No true athlete would skip training"—redefining 'athlete' to protect the claim.

Question 41 Logic And Critical Thinking

What is a hypothesis in the scientific method?

An informal fallacy is an error in reasoning whose flaw lies in the content, context, or delivery of the argument rather than its logical form. A hypothesis is a testable, falsifiable prediction about the relationship between variables, formulated before experimentation. The ad hominem fallacy attacks the person making the argument rather than the argument itself. Example: "You can't trust John's climate data—he's not even a scientist." false only when both are false.

Question 42 Logic And Critical Thinking

What is the appeal to emotion fallacy?

Claiming something is true because an authority figure says so, especially when the authority is not an expert in the relevant field or when experts disagree. ∃x P(x) means "there exists at least one x for which P(x) is true." Manipulating emotions (fear, pity, anger) to win an argument rather than using logical evidence. An argument where the conclusion is assumed in one of the premises. Example: "The Bible is true because it is the word of God, and we know it is the word of God because the Bible says so."

Question 43 Logic And Critical Thinking

Give an example of deductive reasoning.

An argument where the conclusion is assumed in one of the premises. Example: "The Bible is true because it is the word of God, and we know it is the word of God because the Bible says so." The contrapositive of P → Q is ¬Q → ¬P. A conditional and its contrapositive are logically equivalent. A valid argument is one where if all the premises are true, the conclusion must necessarily be true. Validity concerns logical structure, not actual truth. All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Question 44 Logic And Critical Thinking

How does abductive reasoning differ from inductive reasoning?

The converse of P → Q is Q → P. The converse is not logically equivalent to the original conditional. Abductive reasoning selects the best explanation for given data, while inductive reasoning generalizes from specific instances to broader rules. An experiment where one variable is changed (independent variable) while others are kept constant, and results are compared with a control group to isolate causal effects. A proposition cannot be both true and false at the same time and in the same sense. (¬(P ∧ ¬P))

Question 45 Logic And Critical Thinking

What is the bandwagon fallacy (argumentum ad populum)?

Assuming the truth must be a compromise between two opposing positions, regardless of the evidence for each side. A truth table is a mathematical table used to determine the truth value of a compound proposition for every possible combination of truth values of its components. The tendency to believe, after an event has occurred, that one "knew it all along", making outcomes seem more predictable than they were. Arguing that something is true or good because many people believe it or do it.

Question 46 Logic And Critical Thinking

What is a counterexample?

A process where scientific work is evaluated by independent experts in the field before publication, to check methodology, accuracy, and significance. It guides scientists to prefer the simplest explanation that accounts for the evidence, reducing the risk of overfitting and unnecessary complexity. A counterexample is a specific case that disproves a universal claim. One genuine counterexample is sufficient to refute a generalization. All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises.

Question 47 Logic And Critical Thinking

What is the appeal to authority fallacy (argumentum ad verecundiam)?

The ability for an experiment or study to be repeated by others with the same results, which is essential for confirming scientific findings. A non sequitur is an argument in which the conclusion does not logically follow from the premises. Assuming that what is true of the whole must be true of each part. Example: "The university is prestigious, so every department must be prestigious." Claiming something is true because an authority figure says so, especially when the authority is not an expert in the relevant field or when experts disagree.

Question 48 Logic And Critical Thinking

What does falsifiability mean (Karl Popper)?

A statement is falsifiable if there exists a possible observation or experiment that could prove it false. Popper argued this is what distinguishes science from non-science. The major term (predicate of conclusion), minor term (subject of conclusion), and middle term (appears in both premises but not the conclusion). All mammals are warm-blooded. Dogs are mammals. Therefore, dogs are warm-blooded. The conclusion follows necessarily from the premises. A biconditional (P ↔ Q) is true when both P and Q have the same truth value (both true or both false).

Question 49 Logic And Critical Thinking

What is the null hypothesis?

¬(P ∧ Q) ≡ (¬P ∨ ¬Q) and ¬(P ∨ Q) ≡ (¬P ∧ ¬Q). Negating a conjunction gives a disjunction of negations, and vice versa. Cherry-picking data clusters to suit a hypothesis after the fact—like drawing a target around bullet holes. It ignores the data that doesn't fit. The default assumption that there is no effect or no relationship between variables. Experiments aim to gather evidence to reject or fail to reject it. Q is true; therefore P is true. This is invalid because Q could be true for reasons other than P.

Question 50 Logic And Critical Thinking

What is a conclusion in an argument?

Ignoring the general prevalence (base rate) of an event when evaluating probability, and focusing instead on specific but less informative evidence. Assuming that what is true of the whole must be true of each part. Example: "The university is prestigious, so every department must be prestigious." The conclusion is the statement that the premises of an argument are intended to support or prove. A method of updating the probability of a hypothesis based on new evidence using Bayes' theorem: P(H|E) = P(E|H) × P(H) / P(E).