DEDUCTIVE AND INDUCTIVE REASONING: EXPLAINED ANSWER KEY

All cases are fictional. Classification uses the explicitly described classroom convention; ordinary arguments may require further reconstruction.

Case 1: Deductive; valid. P1 and P2 are the premises; C is the conclusion.
If both premises are true, L cannot be an uncatalogued document in that cabinet. The inference applies a universal rule to one member. That establishes validity, not whether the archive actually keeps its promise. To call the argument sound, you would also need true premises. Finding a different uncatalogued document would challenge P1, rather than this inference form.

Case 2: Deductive attempt; invalid. The form affirms the consequent.
P1 provides one sufficient condition for permission, not the only condition. Counterexample: Jo has no valid badge but has an authorized visitor pass. Entry is permitted, so P2 is true; the valid-badge rule remains true, so P1 is true; C is false. This tests the connection between the premises and conclusion. It does not assert that a real venue uses these rules.

Case 3: Deductive attempt; invalid. The form denies the antecedent.
The rule does not say that only the heater can light the indicator. Imagine the heater is off while an indicator-test function lights it. Both premises are true and C is false. A different premise, “The indicator is lit only if the heater is on,” would block that counterexample, but it is absent. Do not repair the argument silently by reversing its conditional.

Case 4: Deductive; valid, although both premises and the conclusion are general.
Any senior member is registered by P1 and has signed by P2. A senior member who had not signed would violate at least one premise. This defeats the shortcut that deduction must always move from a general rule to a particular person. Whether the membership and signature records make P1 and P2 true is a separate factual check.

Case 5: Deductive; valid in form, but unsound in the supplied fictional inventory.
The form is the same as case 1: every K is R; this token is K; therefore it is R. Its validity concerns what would follow if both premises were true. Here P1 is false: the inventory includes a blue, non-red token. P2 is true and C is false in that inventory. A false conclusion does not, by itself, prove an invalid form; a false premise can explain it.

Case 6: Deductive; valid because the roster is explicitly complete.
P1 closes the population: there cannot be another registered student left unexamined. P2–P4 cover every member, so C follows. The move from named individuals to a general conclusion does not make this induction. If P1 merely said that Ari, Bo and Cy are three registered students, an additional student who had not submitted would be a counterexample. The word “only” does important work.

Case 7: Inductive; the stated sampling procedure provides support for the population estimate.
The conclusion concerns 900 members not surveyed. A random sample with complete responses is a better basis than asking only convenient friends, but its result does not logically require a population majority. The unasked members could, in principle, mostly prefer evenings. Check sampling, response and question wording before generalizing. No numerical confidence level is calculated here, and 90% in the sample is not an exact population result.

Case 8: Inductive; weak support for this club-wide conclusion because the sample is narrow and biased.
The respondents were chosen from a group whose schedule already favors evenings. Counting their agreement does not remove that selection problem. A counter-situation is a large morning-preferring membership alongside these five evening-preferring friends: P1 remains true while the club-wide majority claim is false. That possibility alone does not refute all induction; the specific selection mechanism explains why this estimate is poorly supported.

Case 9: Inductive prediction; strongly supported under the stated draw model, but not guaranteed.
The model gives red a probability of 90/100, or 0.9. Nevertheless, any one of the ten blue tokens could be drawn while both premises remain true. A blue outcome would therefore not show that the stated probability model was contradicted. The conclusion predicts a colour, rather than calculating a probability; compare case 11, which uses the same bag for a different claim.

Case 10: Inductive; a past pattern supports a tentative prediction, with important missing conditions.
C reaches beyond the departures actually recorded. Past punctuality can be relevant, but it gives no guarantee about the next departure. A changed timetable, maintenance or disruption could matter without falsifying P1. The statement supplies no method for estimating the next departure’s exact probability. A careful answer names the pattern and the missing stability assumption, rather than turning 20 successful observations into certainty.

Case 11: Deductive; valid within the stated finite, equally likely probability model.
There are 90 favorable tokens among 100 equally likely possibilities: 90/100 = 9/10. This conclusion states a probability, rather than insisting that the actual token must be red. A blue draw does not make the probability claim false. A tampered draw could instead challenge P2. Probability vocabulary does not automatically make an inference inductive; examine exactly what conclusion follows from which premises.

Case 12: Insufficient information for a confident intended classification or a well-supported conclusion.
As written, P1 does not entail C: an empty, closed room is a counterexample to a deductive guarantee. No frequency evidence is supplied for judging a probabilistic connection. A strict rule that the door is closed only during meetings would supply one possible deductive reconstruction; a reliable observed pattern could supply an inductive one. Neither premise is stated. Record the gap and ask what connects a closed door to a meeting.

Source: https://iep.utm.edu/deductive-inductive-arguments/