Analyze the four conditional arguments below. Match each argument (left) with the specific missing assumption (right) that is logically sufficient to bridge the gap between the argument's premises and its conclusion.
- A municipality is eligible for the state urban renewal grant only if its population density exceeds 5,000 residents per square mile. The municipality of Springfield recently constructed three expansive suburban housing developments. Therefore, Springfield is not eligible for the state urban renewal grant.Any municipality that recently constructed three expansive suburban housing developments has a population density that does not exceed 5,000 residents per square mile.
- Unless a pharmaceutical company completes a comprehensive Phase III clinical trial, its novel therapeutic drug will not be approved by the federal regulatory board. Apex Pharma's novel cardiovascular drug was officially approved by the board today. Thus, Apex Pharma's drug must have been tested on a genetically diverse patient population.Every novel therapeutic drug that has completed a comprehensive Phase III clinical trial has been tested on a genetically diverse patient population.
- Any biomedical research project that utilizes CRISPR-edited embryonic stem cells requires rigorous federal oversight to proceed legally. Dr. Aris's current neurological research project does not require rigorous federal oversight to proceed legally. Therefore, Dr. Aris's current project is not funded by the National Science Institute.All biomedical research projects that are funded by the National Science Institute utilize CRISPR-edited embryonic stem cells.
- If an autonomous vehicle's navigation system relies exclusively on optical cameras, it will fail to operate safely in severely inclement weather. The newly released Zenith self-driving car operates perfectly safely in severely inclement weather. Therefore, the Zenith car must incorporate active lidar sensor technology.Any autonomous vehicle's navigation system that does not rely exclusively on optical cameras incorporates active lidar sensor technology.
Answer
Argument 1 pairs with Assumption 1, Argument 2 with Assumption 2, Argument 3 with Assumption 3, and Argument 4 with Assumption 4.
Each argument contains a stranded premise and a conclusion that requires a specific conditional link to be logically valid. By applying the contrapositive and properly diagramming the conditional indicators ('unless', 'only if', 'any', 'if'), the exact missing sufficient assumption can be identified and mapped to each argument.
Step-by-Step Solution
Key Concept
Assumptions in Conditional Logic
Estimated Time:3m 0s