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Zorluk: OrtaMust Be True Questions

According to the recent interstellar survey of the Orionis sector:

All rogue planets detected in the outer ring possess a dense atmosphere of frozen methane. Any planet with a dense atmosphere of frozen methane reflects less than 5% of incident starlight. Most rogue planets detected in the outer ring have a core temperature below -200 degrees Celsius. Furthermore, no planet that reflects less than 5% of incident starlight is currently targeted for deep-core drilling.

Based strictly on the information above, which of the following statements must be true? (Select all valid deductions)

  1. Every rogue planet detected in the outer ring is currently excluded from deep-core drilling targets.Cevap
  2. B
    Any planet that is not a rogue planet detected in the outer ring reflects 5% or more of incident starlight.
  3. C
    Most planets that reflect less than 5% of incident starlight are rogue planets detected in the outer ring.
  4. Any planet that is targeted for deep-core drilling reflects 5% or more of incident starlight.Cevap
  5. E
    Most planets that possess a dense atmosphere of frozen methane have a core temperature below -200 degrees Celsius.

Cevap

The correct deductions are that every rogue planet in the outer ring is excluded from deep-core drilling targets, and that any planet targeted for deep-core drilling reflects 5% or more of incident starlight.
The valid deductions rely on strict conditional logic. By chaining the premises, we find that being an outer ring rogue planet guarantees a frozen methane atmosphere, which guarantees reflecting less than 5% of starlight, which in turn guarantees exclusion from drilling targets. Therefore, any such rogue planet is excluded. Additionally, the contrapositive of the final premise dictates that if a planet IS targeted for drilling, it cannot reflect less than 5% of starlight (meaning it must reflect 5% or more).

Adım Adım Çözüm

1
Map the primary conditional chain provided in the stimulus.
Rogue Planet in Outer Ring (RP) -> Frozen Methane (FM) -> Reflects < 5% Light (<5L).
This establishes the basic transitive relationship from the first two premises.
2
Add the final conditional premise to the chain.
RP -> FM -> <5L -> NOT Targeted for Drilling (~TD).
The final premise introduces a negative necessary condition based on the light reflection.
3
Evaluate the beginning and end of the completed conditional chain.
RP -> ~TD (If a planet is a rogue planet in the outer ring, it is not targeted for drilling).
This proves that the statement claiming every rogue planet in the outer ring is excluded from drilling targets must be logically true.
4
Form the contrapositive of the relationship between light reflection and drilling targets.
The original rule is: If <5L -> ~TD. The contrapositive is: If TD -> NOT <5L (meaning 5% or more).
This proves that the statement claiming any targeted planet reflects 5% or more starlight must be logically true.

Anahtar Kavram

Transitive conditional reasoning and contrapositive formation
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Must Be True Questions

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