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Zorluk: OrtaMust Be True Questions

Every residential development project approved by the City Council this year includes a minimum of 15% affordable housing units. Furthermore, most of the residential development projects approved by the City Council this year rely on municipal tax subsidies. However, the City Council strictly enforces a policy that no project relying on municipal tax subsidies can be located in the historic district.

Based on the information above, which one of the following statements must logically be true?

  1. At least some residential development projects that include a minimum of 15% affordable housing units are not located in the historic district.Cevap
  2. B
    If a residential development project is not located in the historic district, it must rely on municipal tax subsidies.
  3. C
    Any residential development project that does not rely on municipal tax subsidies is located in the historic district.
  4. D
    No residential development projects located in the historic district were approved by the City Council this year.
  5. E
    Most residential development projects that include a minimum of 15% affordable housing units rely on municipal tax subsidies.

Cevap

At least some residential development projects that include a minimum of 15% affordable housing units are not located in the historic district.
The stimulus establishes three facts: First, all approved projects have at least 15% affordable housing. Second, most approved projects rely on tax subsidies. This means there is a specific group of approved projects that feature both affordable housing and subsidies. Third, no project with subsidies is located in the historic district. By combining these facts, the projects that have both affordable housing and subsidies are prohibited from being in the historic district. Therefore, it is mathematically guaranteed that at least some projects with a minimum of 15% affordable housing are not in the historic district.

Adım Adım Çözüm

1
Map the formal logic rules established by the stimulus.
Rule 1: All Approved -> Affordable. Rule 2: Most Approved -> Subsidies. Rule 3: Subsidies -> NOT Historic.
Deconstructing the text into strict conditional and quantified relationships is required to find valid deductions safely.
2
Combine the 'All' and 'Most' statements sharing the same sufficient condition.
Because all approved projects are affordable, and most of them have subsidies, there is an intersection: at least some projects that are affordable also have subsidies.
When a group entirely possesses one trait and mostly possesses a second trait, the two traits must overlap on at least some members.
3
Apply the absolute conditional rule to the intersection group.
Since those overlapping projects have subsidies, Rule 3 dictates they cannot be in the historic district. Thus, some affordable projects are not in the historic district.
Connecting an absolute rule to an established subgroup yields a 100% provable conclusion.

Anahtar Kavram

Formal logic deductions involving conditional statements and overlapping quantifiers.
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Must Be True Questions

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