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Difficulty: MediumCannot Be True Questions

Any commercial aircraft manufactured by AeroStar is equipped with the new Zenith navigation system. An aircraft requires a specialized maintenance team on site to undergo its routine inspections if it is equipped with the Zenith navigation system. The municipal airport in Grandville does not have any specialized maintenance teams on site.

Based on these statements, the following scenario cannot be true: A commercial aircraft manufactured by AeroStar undergoes a routine inspection at the municipal airport in Grandville.

Answer: Answer

Answer

The statement is true because the provided scenario is logically impossible based on the given conditional rules.
The scenario directly contradicts the deduced contrapositive. Since any AeroStar aircraft requires a specialized team on site, and Grandville does not have one, the event cannot occur.

Step-by-Step Solution

1
Map the first two conditional statements to form a chain.
AeroStar aircraft -> Zenith system. Zenith system -> specialized maintenance team on site. Combined: AeroStar aircraft -> specialized maintenance team on site.
Linking conditional statements is the standard method for determining what must be true or what cannot be true in deductive logic.
2
Apply the contrapositive using the information about Grandville.
Grandville airport -> NO specialized maintenance team on site. Therefore, NO Zenith system, which means NOT an AeroStar aircraft undergoing inspection.
The definitive absence of a necessary condition guarantees the absence of the sufficient conditions that rely upon it.
3
Evaluate the proposed scenario against the deductive proof.
The scenario places an AeroStar aircraft undergoing a routine inspection at a location that strictly cannot support it, creating a direct contradiction.
A scenario that contradicts a valid deductive inference drawn from the premises cannot be true.

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