Question

Difficulty: MediumMust Be True Questions

According to the revised aviation safety guidelines, any commercial aircraft operating in polar regions must be equipped with dual-band thermal radar. Furthermore, any aircraft equipped with dual-band thermal radar undergoes rigorous cryogenic calibration every six months. Skyways Airlines recently announced that its entire fleet of cargo planes undergoes rigorous cryogenic calibration every six months.

Statement: Based on the information provided, it must be true that Skyways Airlines operates its cargo planes in polar regions.

Answer: Answer

Answer

False. The proposed statement is not a valid deduction because it relies on an illegal reversal of the conditional premises.
The conclusion drawn in the statement relies on a classic formal logic error. The premises establish a one-way chain: operating in polar regions requires cryogenic calibration. We are told Skyways Airlines undergoes cryogenic calibration. However, we cannot read a conditional statement backward. It is entirely possible that aircraft operating in other regions also undergo cryogenic calibration for different reasons. Thus, it is not logically required that Skyways operates in polar regions, making the 'must be true' claim false.

Step-by-Step Solution

1
Diagram the first conditional premise.
Polar Region → Dual-Band Thermal Radar.
The word 'any' introduces a sufficient condition. If an aircraft operates in polar regions, it is logically required to have the radar.
2
Diagram the second conditional premise.
Dual-Band Thermal Radar → Cryogenic Calibration.
Again, 'any' indicates that having the radar is sufficient to guarantee the aircraft undergoes the calibration.
3
Combine the conditional premises into a chain.
Polar Region → Dual-Band Thermal Radar → Cryogenic Calibration.
Transitive logic allows us to connect the common term to deduce the overarching rule: Polar Region → Cryogenic Calibration.
4
Evaluate the new factual information about Skyways Airlines against the established conditional chain.
We know Skyways Cargo Planes → Cryogenic Calibration. This matches the necessary condition of our chain.
To determine what 'must be true', we must see if the factual premise forces a logical deduction.
5
Determine if the statement is a logically valid deduction.
The statement concludes that Skyways operates in polar regions. This deduction is invalid.
Affirming the necessary condition (calibration) does not prove the sufficient condition (polar operation). Therefore, it does not have to be true that Skyways operates in polar regions.

Key Concept

Evaluating conditional reasoning chains and identifying illegal reversals (affirming the consequent).
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