Examkin

Question

Difficulty: Very hardApplication of Principles

A city council should approve a commercial development in the historic district only if the development preserves the original facades of all existing structures. Furthermore, the development should be approved only if it meets at least one of the following two conditions: it provides affordable housing units, or it does not require a municipal tax subsidy. However, if a development preserves the original facades, provides affordable housing, and does not require a tax subsidy, the council must approve it.

Which one of the following judgments most closely conforms to the principle stated above?

  1. A
    The Apex Building development preserved the original facades of all existing structures and provided affordable housing units. Therefore, the city council was required to approve the Apex Building development.
  2. B
    The Horizon Plaza development did not provide affordable housing units and required a municipal tax subsidy. Therefore, the Horizon Plaza development did not preserve the original facades of all existing structures.
  3. The Silver Tower development was approved by the city council but required a municipal tax subsidy. Therefore, the Silver Tower development must have provided affordable housing units and preserved the original facades of all existing structures.Answer
  4. D
    The city council did not approve the Crestview development, even though it preserved the original facades of all existing structures. Therefore, the Crestview development must have failed to provide affordable housing units and required a municipal tax subsidy.
  5. E
    The city council approved the Beacon Complex, and the development provided affordable housing units. Therefore, the Beacon Complex must not have required a municipal tax subsidy.

Answer

The judgment regarding the Silver Tower development, which concludes that because it was approved but required a municipal tax subsidy, it must have provided affordable housing units and preserved the original facades.
The correct answer accurately applies the necessary conditions for approval established in the stimulus. We are told that approval requires preserving original facades AND either providing affordable housing or not requiring a tax subsidy. Because this specific development was approved, all of these necessary conditions must have been met. Since it did require a tax subsidy, it failed one half of the 'either/or' condition. Therefore, to satisfy the logical requirement, it absolutely must have fulfilled the other half by providing affordable housing. It also must have met the baseline requirement of preserving the original facades.

Step-by-Step Solution

1
Diagram the necessary conditions for approval.
Approval (A) → Preserves Facades (PF) AND [Provides Affordable Housing (AH) OR Does Not Require Subsidy (~TS)]
The phrase 'only if' introduces necessary conditions that must be met for approval to be granted.
2
Diagram the sufficient condition for approval.
(PF AND AH AND ~TS) → Approval (A)
The phrase 'if' introduces a sufficient condition, and 'must approve it' establishes the guaranteed outcome.
3
Analyze the correct judgment using the established necessary conditions.
The Silver Tower was approved (A is true). Therefore, PF must be true, AND the disjunction (AH OR ~TS) must be true.
When a sufficient condition (Approval) is met, all of its necessary conditions are guaranteed to occur.
4
Evaluate the disjunction based on the provided facts.
The Silver Tower required a municipal tax subsidy, meaning ~TS is false. For the statement (AH OR ~TS) to remain true, AH must be true.
In formal logic, if an 'OR' statement is true but one of its components is false, the other component must definitively be true.
5
Conclude the final logical requirement.
The development must have preserved facades (PF) AND provided affordable housing (AH).
This perfectly matches the deductive conclusion drawn in the correct judgment.

Key Concept

Applying complex formal logic, specifically tracking compound necessary and sufficient conditions, evaluating disjunctions (OR statements), and forming proper contrapositives.
Rate this question

Topics

Application of Principles

More questions from this topic