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Zorluk: Çok zorMust Be True / Most Strongly Supported

Urban planners for the city of Oakhaven have established the following zoning regulations and observations: Any residential parcel zoned for high-density development must be located within 500 meters of a rapid transit station. Furthermore, if a parcel is located within 500 meters of a rapid transit station and is also zoned for commercial mixed-use, it automatically qualifies for a parking minimum exemption. Currently, no parcels zoned for high-density development qualify for a parking minimum exemption. Finally, most parcels zoned for commercial mixed-use in the downtown district are located within 500 meters of a rapid transit station.

Based on the information above, which of the following statements must be true? (Select all that apply)

  1. No residential parcel zoned for high-density development is also zoned for commercial mixed-use.Cevap
  2. At least some parcels located within 500 meters of a rapid transit station are not zoned for high-density development.Cevap
  3. C
    If a parcel qualifies for a parking minimum exemption, it must be located within 500 meters of a rapid transit station.
  4. D
    Most parcels located within 500 meters of a rapid transit station qualify for a parking minimum exemption.
  5. E
    Any parcel that is zoned for commercial mixed-use but is not located within 500 meters of a rapid transit station cannot qualify for a parking minimum exemption.

Cevap

The statements that must be true are that no high-density parcel is commercial mixed-use, and that some transit-adjacent parcels are not high-density.
The correct statements reflect logical certainties derived directly from the text. First, because high-density parcels must be near transit, making them commercial mixed-use would trigger an exemption they explicitly do not have; thus, they cannot be commercial mixed-use. Second, because most downtown commercial mixed-use parcels are near transit, and we know they cannot be high-density, it guarantees that at least some transit-adjacent parcels are not high-density.

Adım Adım Çözüm

1
Map the formal logic conditionals from the stimulus.
1: High-Density (HD) -> Near Transit (NT). 2: (NT + Commercial Mixed-Use (CMU)) -> Exemption (E). 3: HD -> ~E. 4: Downtown CMU -most-> NT.
Mapping the premises allows for precise deduction without relying on outside assumptions.
2
Combine premises 1, 2, and 3 to find overlapping conditions.
If a parcel is HD, it is NT. If it were also CMU, it would be NT + CMU, triggering E. But premise 3 says HD -> ~E.
Testing intersection of categories reveals impossible combinations.
3
Deduce the relationship between HD and CMU.
Because being both HD and CMU leads to a contradiction (qualifying for E and not qualifying for E), a parcel cannot be both. Thus, No HD is CMU.
Resolving the contradiction establishes the first objectively true statement.
4
Apply the new deduction to the proportional premise (premise 4).
Since Downtown CMU -most-> NT, there is at least one (in fact, many) NT parcel that is CMU. Since no CMU is HD, these specific NT parcels are not HD.
Combining a 'most' statement with a negative absolute statement yields a 'some are not' deduction.

Anahtar Kavram

Conditional Logic Chaining and Quantifier Intersections
Tahmini Süre:3m 0s
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Konular

Must Be True / Most Strongly Supported

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