Watson-Glaser Critical Thinking Appraisal Drawing Deductive Conclusions 4 — Questions and Answers
Question 1: Premise: No city in Region A has a population under 50,000. Premise: Millbrook is a city in Region A. Conclusion: Millbrook has a population of at least 50,000. Is this conclusion valid?
- The conclusion does not follow — Millbrook could be newly incorporated.
- The conclusion follows — the universal negative leaves no exceptions for Region A cities. (Correct answer)
- The conclusion follows only if the census data is current.
- The conclusion does not follow — population thresholds change over time.
Correct answer: The conclusion follows — the universal negative leaves no exceptions for Region A cities.
Because no city in Region A has a population under 50,000 and Millbrook is a city in Region A, Millbrook must have at least 50,000 people.
Question 2: Premise: All board members who attended the summit signed the agreement. Premise: Director Chen did not sign the agreement. Conclusion: Director Chen did not attend the summit. Is this conclusion valid?
- The conclusion does not follow — Director Chen may have signed a different document.
- The conclusion follows — not signing is proof of non-attendance given the premise. (Correct answer)
- The conclusion follows only if Director Chen is a full board member.
- The conclusion does not follow — signing may have been voluntary.
Correct answer: The conclusion follows — not signing is proof of non-attendance given the premise.
Since attending the summit guarantees signing, the absence of a signature (contrapositive) guarantees non-attendance.
Question 3: Premise: Either the server is overloaded or the network is down. Premise: The server is not overloaded. Conclusion: The network is down. Is this conclusion valid?
- The conclusion does not follow — both conditions could be false simultaneously.
- The conclusion follows — eliminating one disjunct in an either/or statement forces the other. (Correct answer)
- The conclusion follows only if both causes were active previously.
- The conclusion does not follow — other causes of the problem exist.
Correct answer: The conclusion follows — eliminating one disjunct in an either/or statement forces the other.
An 'either/or' premise guarantees at least one is true; ruling out the server being overloaded means the network must be down.
Question 4: Premise: All registered voters in Precinct 7 received a ballot. Premise: Ms. Rivera received a ballot. Conclusion: Ms. Rivera is a registered voter in Precinct 7. Is this conclusion valid?
- The conclusion follows — only registered voters receive ballots.
- The conclusion does not follow — ballots may have been distributed to other groups as well. (Correct answer)
- The conclusion follows if Ms. Rivera lives in Precinct 7.
- The conclusion does not follow — she may have received a provisional ballot.
Correct answer: The conclusion does not follow — ballots may have been distributed to other groups as well.
The premise says registered voters received ballots, not that receiving a ballot is exclusive to registered voters in Precinct 7; others may have also received ballots.
Question 5: Premise: Every product recalled by the agency contained defective components. Premise: Product X was recalled by the agency. Conclusion: Product X contained defective components. Is this conclusion valid?
- The conclusion follows — the universal rule covers every recalled product, including Product X. (Correct answer)
- The conclusion does not follow — recalls can occur for labeling errors.
- The conclusion follows only if Product X was recalled voluntarily.
- The conclusion does not follow — 'defective' is a subjective term.
Correct answer: The conclusion follows — the universal rule covers every recalled product, including Product X.
Since every recalled product contained defective components and Product X was recalled, it necessarily follows that Product X contained defective components.
Question 6: Premise: No athletes in the league tested positive for banned substances this year. Premise: Jordan competes in the league. Conclusion: Jordan did not test positive for banned substances this year. Is this conclusion valid?
- The conclusion does not follow — Jordan may have missed testing.
- The conclusion follows — the universal negative includes Jordan as a league athlete. (Correct answer)
- The conclusion follows only if Jordan was tested.
- The conclusion does not follow — the premise covers most, not all, athletes.
Correct answer: The conclusion follows — the universal negative includes Jordan as a league athlete.
The premise states no athlete in the league tested positive, and Jordan is a league athlete, so it follows necessarily that Jordan did not test positive.
Question 7: Premise: If tuition increases by more than 5%, enrollment will decline. Premise: Enrollment did not decline. Conclusion: Tuition did not increase by more than 5%. Is this conclusion valid?
- The conclusion does not follow — enrollment could decline later.
- The conclusion follows — it is the valid contrapositive of the conditional premise. (Correct answer)
- The conclusion follows only if enrollment data is final.
- The conclusion does not follow — tuition and enrollment are independent.
Correct answer: The conclusion follows — it is the valid contrapositive of the conditional premise.
The contrapositive of 'if P then Q' is 'if not Q then not P,' which is logically equivalent; since enrollment did not decline, tuition did not increase by more than 5%.
Watson-Glaser Critical Thinking Appraisal Drawing Deductive Conclusions 4
Premise: No city in Region A has a population under 50,000.
Premise: Millbrook is a city in Region A.
Conclusion: Millbrook has a population of at least 50,000.
Is this conclusion valid?