OACP Deductive and Inductive Reasoning 3 — Questions and Answers
Question 1: During the OACP test, a passage states: 'Experienced officers always file complete reports. Constable Rivera is experienced.' What must be true?
- Constable Rivera sometimes files complete reports
- Constable Rivera files complete reports (Correct answer)
- Constable Rivera is the best report writer
- Constable Rivera was recently promoted
Correct answer: Constable Rivera files complete reports
The universal premise combined with the specific premise deductively guarantees the conclusion.
Question 2: Which of the following best illustrates affirming the consequent — an invalid deductive form?
- If it is arson, there will be accelerant. There is accelerant. Therefore it is arson. (Correct answer)
- If it is arson, there will be accelerant. There is no accelerant. Therefore it is not arson.
- All arsons involve accelerant. This fire has no accelerant. Therefore it is not arson.
- Some fires involve accelerant. This fire has accelerant. Therefore it might be arson.
Correct answer: If it is arson, there will be accelerant. There is accelerant. Therefore it is arson.
Affirming the consequent is invalid because other causes could explain the presence of accelerant.
Question 3: A criminologist reviews records and notes that 85% of repeat offenders in a district were previously convicted of theft. She infers that theft history is a risk factor for reoffending. This reasoning is:
- Deductive and certain
- Inductive and probabilistic (Correct answer)
- Syllogistic and absolute
- Axiomatic and universal
Correct answer: Inductive and probabilistic
Statistical patterns drawn from records form an inductive, probabilistic inference rather than a certain deductive conclusion.
Question 4: An officer's logic: 'Either the witness is lying or mistaken. The witness is not lying. Therefore the witness is mistaken.' This argument uses:
- Hypothetical syllogism
- Disjunctive syllogism (Correct answer)
- Modus ponens
- Inductive generalization
Correct answer: Disjunctive syllogism
Disjunctive syllogism eliminates one option from an either/or premise to confirm the other.
Question 5: In OACP reading comprehension, you encounter: 'Most community policing initiatives reduce fear of crime. Initiative X is a community policing initiative.' The BEST conclusion is:
- Initiative X will definitely reduce fear of crime
- Initiative X will probably reduce fear of crime (Correct answer)
- Initiative X will not reduce fear of crime
- Initiative X is unrelated to fear of crime
Correct answer: Initiative X will probably reduce fear of crime
'Most' signals an inductive premise, so the conclusion is probable rather than certain.
Question 6: A supervisor notices five new recruits all struggled with night-shift paperwork in their first month and concludes that all recruits need extra paperwork training at night. This is an example of:
- Deductive reasoning from policy
- Hasty generalization — a weak inductive fallacy (Correct answer)
- Valid modus tollens
- Sound hypothetical syllogism
Correct answer: Hasty generalization — a weak inductive fallacy
Drawing a universal conclusion from a small, possibly unrepresentative sample is a hasty generalization.
Question 7: Which chain of reasoning represents a VALID hypothetical syllogism?
- If A then B; B is true; therefore A is true
- If A then B; if B then C; therefore if A then C (Correct answer)
- If A then B; A is false; therefore B is false
- If A then B; C is true; therefore B is true
Correct answer: If A then B; if B then C; therefore if A then C
Hypothetical syllogism chains two conditional statements to produce a valid third conditional conclusion.
