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Difficulty: MediumDiagramming Conditional Statements

According to the new city zoning regulations, a commercial development permit will be approved only if the proposed building features a public green space and adheres strictly to the district's height restrictions. Furthermore, a building cannot adhere to these height restrictions unless its architectural plans undergo a rigorous environmental review.

If the statements above are true, which one of the following must also be true?

  1. If the architectural plans for a proposed building do not undergo a rigorous environmental review, then a commercial development permit will not be approved for it.Answer
  2. B
    If a commercial development permit is not approved for a proposed building, then its architectural plans did not undergo a rigorous environmental review.
  3. C
    If a proposed building features a public green space and adheres to the height restrictions, its commercial development permit will be approved.
  4. D
    A rigorous environmental review is sufficient to ensure that a proposed building adheres to the district's height restrictions.
  5. E
    Any building whose architectural plans undergo a rigorous environmental review must also feature a public green space.

Answer

If the architectural plans for a proposed building do not undergo a rigorous environmental review, then a commercial development permit will not be approved for it.
The correct answer accurately forms the contrapositive of the logical chain provided in the stimulus. By establishing that 'Permit Approved' requires 'Height Restrictions', and 'Height Restrictions' requires 'Environmental Review', we can logically conclude that 'Permit Approved' ultimately requires 'Environmental Review'. The contrapositive of this relationship is that without an environmental review, a permit cannot be approved.

Step-by-Step Solution

1
Diagram the first sentence using the 'only if' indicator.
Permit Approved → Public Green Space AND Adheres to Height Restrictions.
The phrase 'only if' introduces necessary conditions, which go on the right side of the arrow.
2
Diagram the second sentence using the 'cannot... unless' indicator.
Adheres to Height Restrictions → Environmental Review.
The phrase 'unless' introduces a necessary condition. 'Cannot adhere' becomes positive 'Adheres' as the sufficient condition.
3
Link the conditional statements together into a transitive chain.
Permit Approved → Adheres to Height Restrictions → Environmental Review.
Because 'Adheres to Height Restrictions' is necessary for Approval and sufficient for Environmental Review, the chain connects them.
4
Form the contrapositive of the extended conditional chain.
NOT Environmental Review → NOT Permit Approved.
Reversing and negating the ends of the chain yields a valid deduction that matches the correct answer.

Key Concept

Chaining Conditional Statements and Contrapositives
Estimated Time:1m 30s
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Topics

Diagramming Conditional Statements

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