A city planning commission is establishing the zoning regulations for a new urban district. Match each set of proposed conditional zoning rules with the logically valid deduction that must follow from those rules.
- If a district approves retail zoning, it must require public parking facilities. Moreover, any district that requires public parking facilities must contain a subway station.Any district that lacks a subway station cannot approve retail zoning.
- If a district approves retail zoning, it cannot require public parking facilities. Any district that does not require public parking facilities is ineligible to contain a subway station.If a district contains a subway station, it must reject retail zoning.
- If a district rejects retail zoning, it is forced to require public parking facilities. Furthermore, a district can require public parking facilities only if it contains a subway station.Any district that lacks a subway station is guaranteed to approve retail zoning.
- A district will contain a subway station only if it requires public parking facilities. Whenever a district requires public parking facilities, it is guaranteed to approve retail zoning.If a district rejects retail zoning, it cannot contain a subway station.
Answer
The correct matches map each set of conditional premises to its validly chained contrapositive. Left 1 maps to Right 1; Left 2 maps to Right 2; Left 3 maps to Right 3; Left 4 maps to Right 4.
Each correct pair requires diagramming the two explicit premises, connecting them via their shared term to form a transitive chain, and then identifying the contrapositive of that full chain among the available deductions.
Step-by-Step Solution
Key Concept
Chaining Conditional Statements and Contrapositives