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Difficulty: MediumMust Be True Questions

Under the new municipal zoning code, any neighborhood designated as a Transit-Oriented District must allow for high-density residential development. Furthermore, a neighborhood cannot be designated as a Transit-Oriented District unless it currently contains at least one active light-rail station. The code also specifies that any neighborhood allowing for high-density residential development is required to allocate at least 15 percent of its new housing units for low-income residents. The Historic Southside neighborhood recently had its only active light-rail station permanently decommissioned.

Which of the following must be true on the basis of the statements above?

  1. Any neighborhood that is not required to allocate at least 15 percent of its new housing units for low-income residents cannot be designated as a Transit-Oriented District.Answer
  2. B
    Because it no longer contains an active light-rail station, the Historic Southside neighborhood is prohibited from allowing high-density residential development.
  3. C
    Any neighborhood that allocates at least 15 percent of its new housing units for low-income residents and contains an active light-rail station is designated as a Transit-Oriented District.
  4. D
    The primary goal of the new municipal zoning code is to increase the availability of low-income housing near active transit stations.
  5. E
    Most neighborhoods that contain at least one active light-rail station are designated as Transit-Oriented Districts.

Answer

Any neighborhood that is not required to allocate at least 15 percent of its new housing units for low-income residents cannot be designated as a Transit-Oriented District.
The stimulus provides two key conditional statements that can be connected: 'Transit-Oriented District -> high-density residential' and 'high-density residential -> 15 percent low-income'. Linking these statements creates the deduction: 'Transit-Oriented District -> 15 percent low-income'. The correct answer is the logical contrapositive of this deduction: if a neighborhood is not required to allocate 15 percent for low-income housing, it cannot be a Transit-Oriented District.

Step-by-Step Solution

1
Diagram the conditional statements provided in the stimulus.
1) TOD -> HDR
2) TOD -> ALRS (Contrapositive: ~ALRS -> ~TOD)
3) HDR -> 15% LI
4) Historic Southside -> ~ALRS
Translating text into formal logic makes it easier to track relationships and avoid traps.
2
Chain the conditional statements together where possible.
Combining premises 1 and 3 (TOD -> HDR and HDR -> 15% LI) yields the logical chain: TOD -> HDR -> 15% LI. Therefore, TOD -> 15% LI.
Connecting premises reveals hidden logical inferences that must be true.
3
Form the contrapositive of the new logical chain.
The contrapositive of (TOD -> 15% LI) is (~15% LI -> ~TOD).
Correct answers in 'Must Be True' questions are frequently the contrapositive of a chained inference.
4
Evaluate the information about the Historic Southside neighborhood.
Since Historic Southside has no active light-rail station (~ALRS), it cannot be a TOD (~TOD). No further valid deductions can be made about its high-density development or low-income housing.
This confirms that options making claims about Historic Southside's high-density development are likely testing illegal negation.

Key Concept

Conditional Logic Chaining and Contrapositives
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