Logical Reasoning and Analysis Flashcards

A detective reviews the following statements from three witnesses after a warehouse break-in: • Witness 1: 'Either the alarm was disabled before entry OR the perpetrator had inside knowledge — but not both.' • Witness 2: 'The alarm was NOT disabled before entry.' • Witness 3: 'If the perpetrator had inside knowledge, then a current employee is a suspect.' Based strictly on the logical structure of these statements, which conclusion is definitively valid?

Answer: A current employee must be considered a suspect.

Using modus ponens and disjunctive syllogism: Witness 2 establishes the alarm was NOT disabled. Witness 1 presents an exclusive disjunction — since one disjunct is false (alarm disabled), the other must be true: the perpetrator had inside knowledge. Witness 3 then triggers: if inside knowledge → current employee is a suspect. Therefore, a current employee must be considered a suspect. The logical chain is airtight regardless of witness credibility (the question asks about logical structure).

An investigator notes that in a given jurisdiction, 100% of convicted arsonists who used accelerants tested positive for a specific chemical marker on their clothing. During a suspect interview, the investigator reasons: 'This suspect tested positive for the chemical marker, therefore this suspect is an arsonist who used accelerants.' Which logical fallacy does this reasoning commit?

Answer: Affirming the consequent

The original conditional is: IF someone is a convicted arsonist who used accelerants, THEN they test positive for the marker. The investigator reverses this: because the suspect tests positive (the consequent is true), they must be an arsonist (affirming the consequent). This is invalid — the marker could be present for many other reasons. Just because all arsonists have the marker does not mean all people with the marker are arsonists. This is a textbook case of affirming the consequent.

During a use-of-force review board, an officer's decision is evaluated using the following chain of reasoning: P1: Any force that exceeds what a reasonable officer would use in identical circumstances is excessive. P2: Officer Chen used a control technique that 70% of surveyed officers would not have used. P3: Therefore, Officer Chen used excessive force. Which specific flaw undermines this syllogism?

Answer: P2 does not establish that a 'reasonable officer' would not have used the technique, only that most surveyed officers would not.

The standard in P1 is what a 'reasonable officer' would do — a legal and professional standard of competence, not a statistical majority preference. P2 only establishes that 70% of surveyed officers reported they would not have used that technique, which is a preference/survey statistic. It does not logically equate to what a reasonable officer 'would' do under identical circumstances, especially since 30% would have used it, training standards vary, and individual circumstances matter. The syllogism's middle term ('reasonable officer' vs. '70% of surveyed officers') is not logically equivalent, making the argument invalid.

An analyst is building a suspect profile. She establishes the following: (1) Anyone who committed the crime must have been at the docks between 11 PM and 1 AM. (2) Suspect Reyes has an alibi placing him at a restaurant until 11:45 PM with verified credit card records. (3) The restaurant is a 40-minute drive from the docks under optimal conditions. Which of the following represents the MOST logically precise conclusion?

Answer: Reyes cannot be definitively excluded because part of the required window (12:25 AM–1:00 AM) remains unaccounted for.

The crime required presence at the docks between 11 PM and 1 AM. Reyes was at the restaurant until 11:45 PM. With a 40-minute minimum drive, the earliest he could arrive at the docks is 12:25 AM. This means the window from 12:25 AM to 1:00 AM (35 minutes) is entirely unaccounted for. While improbable, Reyes cannot be logically excluded based solely on the information given — he had a narrow but possible window. Option A overstates the alibi's coverage. Option B misstates the logical issue. Option D introduces unsupported speculation about fraud.

A commander reviews a patrol sergeant's report that states: 'We have increased foot patrols in the Millbrook district by 40% over three months, and property crime has dropped 18% in that same period. Therefore, increased foot patrols caused the reduction in property crime.' A senior analyst objects to this conclusion. Which of the following best represents the STRONGEST logical basis for the analyst's objection?

Answer: Correlation between two simultaneous trends does not establish that one caused the other, as multiple confounding variables may explain the crime drop.

The sergeant commits the post hoc ergo propter hoc fallacy (assuming causation from sequence/correlation). Even if both trends are real and simultaneous, the crime drop could be attributable to seasonal variation, economic changes, demographic shifts, concurrent social programs, displacement of crime to other areas, or reporting changes. Without controlling for these variables through a proper comparative analysis, causation cannot be established. Option A is incorrect — 18% could be highly significant depending on baseline. Option C is relevant but weaker than the core logical flaw. Option D is an ad hominem argument.

During an interrogation, an investigator presents this argument to a suspect: 'You told us you were home alone all evening. But your neighbour says she saw your car leave at 9 PM. If you lied about being home, you have something to hide. And if you have something to hide, you're probably guilty. So you're probably guilty.' A supervisor reviewing the transcript identifies two distinct logical problems with this chain. Which answer correctly identifies BOTH problems?

Answer: The inference from 'lied about location' to 'has something to hide' ignores innocent explanations; and 'probably guilty' conflates suspicion with legal guilt.

Two distinct flaws exist: (1) The leap from 'lied about location' to 'has something to hide' ignores numerous innocent explanations — the suspect may have left briefly for an embarrassing but innocent reason, to protect someone else, out of fear, etc. This is an overly narrow interpretation of the evidence. (2) Concluding the suspect is 'probably guilty' from these premises conflates investigative suspicion with actual culpability — guilt is a legal determination that requires a comprehensive evidentiary standard, not a probabilistic chain of inferences from a single inconsistency. Option C's 'circular reasoning' claim is inaccurate — the argument is a causal chain, not circular. Option D's 'false dilemma' and 'appeal to authority' labels do not accurately describe the flaws present.