An academic policy review board is analyzing four distinct arguments to evaluate their underlying deductive forms and fallacies. Match each argument with the statement that accurately characterizes its logical structure or reasoning error.
- Any municipal transit expansion that successfully mitigates downtown traffic congestion requires dedicated bus rapid transit lanes. The proposed crosstown transit expansion includes dedicated bus rapid transit lanes. Therefore, the crosstown transit expansion will definitely mitigate downtown traffic congestion.Inferring that an outcome is guaranteed to occur simply because a condition necessary for that outcome has been satisfied.
- Every regional historical archive that receives state preservation funding must employ a full-time certified archivist. The maritime records repository does not employ a full-time certified archivist. Thus, the maritime records repository does not receive state preservation funding.Deducing that a sufficient condition does not hold on the grounds that a necessary condition entailed by it is absent.
- Most municipal botanical conservatories that installed automated drip-irrigation systems reduced their seasonal water consumption. Furthermore, all conservatories that reduced their seasonal water consumption qualified for regional environmental stewardship grants. Consequently, some municipal botanical conservatories that installed automated drip-irrigation systems qualified for regional environmental stewardship grants.Deriving a valid existential overlap by linking a characteristic shared by a majority of a category through a universal conditional rule.
- Whenever a biomedical clinical trial adheres strictly to double-blind randomized control protocols, its published results are reproducible. The recent pharmacological trial on novel antihypertensive compounds failed to adhere strictly to double-blind randomized control protocols. Hence, the published results of this pharmacological trial are not reproducible.Concluding that an outcome cannot occur solely because an antecedent condition sufficient to guarantee it was not met.
Answer
The municipal transit argument matches the description of treating a necessary condition as sufficient; the historical archive argument matches the valid contrapositive deduction; the botanical conservatory argument matches the valid quantifier overlap; and the biomedical trial argument matches the error of inferring the absence of an outcome from the failure of a sufficient condition.
Each argument is paired with the exact formal logical principle governing its deduction: the transit argument mistakenly treats a necessary condition as sufficient; the archive argument executes a logically sound contrapositive deduction; the conservatory argument demonstrates a valid quantifier chain establishing that some members share a downstream property; and the clinical trial argument fallaciously presumes that failing to satisfy one sufficient condition precludes the result from occurring through other means.
Step-by-Step Solution
Key Concept
Parallel structural and flaw analysis in formal conditional and quantifier logic
Estimated Time:2m 0s