Below are five short arguments concerning the proposed Arcadia transit expansion. Each argument is logically incomplete because it commits a formal reasoning error or lacks a crucial premise. Match each incomplete argument to the specific sufficient assumption that perfectly bridges its logical gap.
- Argument 1: A municipal transit plan will secure federal funding only if it increases daily ridership. The Arcadia proposal centers on implementing automated ticketing, a measure that guarantees an increase in daily ridership. Therefore, the Arcadia proposal will successfully secure federal funding.Any municipal transit plan that successfully increases daily ridership will secure federal funding.
- Argument 2: If a transit plan implements automated ticketing, it will eliminate toll jobs. Furthermore, eliminating toll jobs is a necessary condition for reducing carbon emissions. The Arcadia proposal will definitely eliminate toll jobs. Therefore, the Arcadia proposal involves implementing automated ticketing.Any transit plan that eliminates toll jobs must necessarily involve the implementation of automated ticketing.
- Argument 3: In order to reduce carbon emissions, a transit system must secure federal funding. The Arcadia proposal focuses on implementing automated ticketing, which unfortunately disqualifies it from securing federal funding. Therefore, the Arcadia proposal will eliminate toll jobs.A transit plan will inevitably eliminate toll jobs if it fails to secure federal funding.
- Argument 4: Most transit plans that increase daily ridership also succeed in reducing carbon emissions. By securing federal funding, the Arcadia proposal ensures that it will increase daily ridership. Therefore, the Arcadia proposal will ultimately implement automated ticketing.Every transit plan that increases daily ridership is guaranteed to implement automated ticketing.
- Argument 5: Any transit plan that eliminates toll jobs will fail to secure federal funding unless it also increases daily ridership. The Arcadia proposal eliminates toll jobs but successfully increases daily ridership. Therefore, the Arcadia proposal will succeed in reducing carbon emissions.Any transit plan that simultaneously eliminates toll jobs and increases daily ridership will reduce carbon emissions.
Cevap
Argument 1 matches with the ridership-to-funding assumption. Argument 2 matches with the job-elimination-to-ticketing assumption. Argument 3 matches with the failed-funding-to-job-elimination assumption. Argument 4 matches with the ridership-to-ticketing assumption. Argument 5 matches with the combined job-elimination-and-ridership-to-emissions assumption.
Each correct assumption perfectly completes the deductive bridge by converting the argument's logical gap into a valid modus ponens deduction. By mapping the premises as conditional statements, we isolate the exact trigger needed to force the conclusion to be true.
Adım Adım Çözüm
Anahtar Kavram
Sufficient Assumptions via Formal Logic Mapping
Tahmini Süre:3m 30s