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Difficulty: HardForming Contrapositives

Under the revised municipal zoning regulations, a geothermal energy facility will be granted a commercial operating permit only if it incorporates advanced seismic monitoring equipment and operates within a strict noise threshold.

Based on these regulations, it is logically valid to conclude that if a geothermal energy facility is not granted a commercial operating permit, it must be the case that it either failed to incorporate advanced seismic monitoring equipment or failed to operate within a strict noise threshold.

Answer: Answer

Answer

False
The conclusion is logically invalid because it commits the fallacy of Mistaken Negation. The original premise establishes that the equipment and noise threshold are necessary conditions for a permit. The stem incorrectly infers that lacking a permit guarantees a failure to meet these specific conditions, ignoring the fact that the permit could easily be denied for other reasons.

Step-by-Step Solution

1
Diagram the formal logic in the original premise.
Permit Granted → (Seismic Equipment AND Noise Threshold)
The phrase 'only if' introduces necessary conditions, which must be placed on the right side of the conditional arrow.
2
Form the valid contrapositive of the original premise.
(No Seismic Equipment OR No Noise Threshold) → No Permit Granted
To form a valid contrapositive, reverse the terms, negate them, and apply De Morgan's laws to change 'AND' to 'OR'.
3
Diagram the logical relationship asserted in the stem's conclusion.
No Permit Granted → (No Seismic Equipment OR No Noise Threshold)
Translating the proposed inference allows for direct comparison with the valid contrapositive.
4
Compare the asserted conclusion to the valid contrapositive.
The asserted conclusion is a Mistaken Negation of the original premise.
The conclusion improperly treats the necessary conditions as if they were sufficient, making the logical inference invalid.

Key Concept

Distinguishing a valid contrapositive from a Mistaken Negation when evaluating compound conditional statements.
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Topics

Forming Contrapositives

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