Consider the following principle from a city's architectural preservation guidelines:
A building is eligible for the heritage registry only if it retains its original facade and has not undergone major structural modifications.
The logically valid contrapositive of this principle is: If a building is not eligible for the heritage registry, then it must either not retain its original facade or have undergone major structural modifications.
Answer: Answer
Answer
False
The proposed statement is logically false because it is a Mistaken Negation of the original principle. The original conditional statement is 'If eligible, then retains facade AND no major modifications.' A valid contrapositive must both negate AND reverse the conditions, resulting in 'If does not retain facade OR has major modifications, then not eligible.' The statement provided correctly negates the terms using De Morgan's laws but fails to reverse them, incorrectly inferring the absence of the necessary conditions from the absence of the sufficient condition.
Step-by-Step Solution
Key Concept
Forming contrapositives using De Morgan's laws