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Difficulty: EasyCategorical Classification and Sorting

A commercial real estate development firm categorizes building proposals using two regulatory compliance rules:

1. Zoning Board Review: A proposal is classified as *Required* if the building height exceeds 50 m50\text{ m} OR if the building footprint exceeds 2000 m22{}000\text{ m}^2. Otherwise, it is classified as *Exempt*.
2. Traffic Impact Assessment: A proposal is classified as *Required* if the building height exceeds 40 m40\text{ m} AND the building footprint exceeds 1500 m21{}500\text{ m}^2. Otherwise, it is classified as *Exempt*.

Building Proposal X specifies a building height of 45 m45\text{ m} and a building footprint of 1800 m21{}800\text{ m}^2.

Which of the following correctly pairs the classification for Zoning Board Review and Traffic Impact Assessment for Building Proposal X?

  1. Zoning Board Review: Exempt; Traffic Impact Assessment: RequiredAnswer
  2. B
    Zoning Board Review: Required; Traffic Impact Assessment: Exempt
  3. C
    Zoning Board Review: Required; Traffic Impact Assessment: Required
  4. D
    Zoning Board Review: Exempt; Traffic Impact Assessment: Exempt
  5. E
    Zoning Board Review: Required; Traffic Impact Assessment: Conditional

Answer

Zoning Board Review: Exempt; Traffic Impact Assessment: Required
Evaluating Proposal X (45 m45\text{ m} height, 1800 m21{}800\text{ m}^2 footprint) under Rule 1 shows that neither 45>5045 > 50 nor 1800>20001{}800 > 2{}000 holds true, making Zoning Board Review Exempt. Under Rule 2, both 45>4045 > 40 and 1800>15001{}800 > 1{}500 hold true, making Traffic Impact Assessment Required. The option pairing 'Exempt' for Zoning Board Review and 'Required' for Traffic Impact Assessment is correct.

Step-by-Step Solution

1
Evaluate the condition for Zoning Board Review
Building height is 45 m45\text{ m} (not >50 m> 50\text{ m}) and footprint is 1800 m21{}800\text{ m}^2 (not >2000 m2> 2{}000\text{ m}^2). Since neither condition of the OR clause is satisfied, Zoning Board Review is Exempt.
An OR logical rule requires at least one condition to be true for the designation to apply.
2
Evaluate the condition for Traffic Impact Assessment
Building height is 45 m45\text{ m} (>40 m> 40\text{ m}) and footprint is 1800 m21{}800\text{ m}^2 (>1500 m2> 1{}500\text{ m}^2). Since both conditions of the AND clause are satisfied, Traffic Impact Assessment is Required.
An AND logical rule requires all specified conditions to be met simultaneously.
3
Combine the evaluations into the paired result
Zoning Board Review: Exempt; Traffic Impact Assessment: Required
Matching both calculated categorical outcomes with the choices provided.

Key Concept

Categorical classification using logical conjunctions (AND) and disjunctions (OR)
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Topics

Categorical Classification and Sorting

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