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Zorluk: Çok zorDiagramming Conditional Statements

According to interstellar quarantine protocols, a celestial body is designated as a Class-Alpha hazard only if it harbors extremophile bacteria or emits anomalous radiation. No celestial body without a stable magnetosphere can harbor extremophile bacteria. Furthermore, emitting anomalous radiation requires a subterranean thermal vent, and any celestial body with a subterranean thermal vent possesses a stable magnetosphere. Finally, unless a celestial body features a crystalline core, it cannot have a stable magnetosphere.

Which one of the following statements logically follows from the quarantine protocols?

  1. A
    If a celestial body features a crystalline core, it must be designated as a Class-Alpha hazard.
  2. B
    If a celestial body is not designated as a Class-Alpha hazard, it cannot possess a stable magnetosphere.
  3. Any celestial body that does not feature a crystalline core cannot be designated as a Class-Alpha hazard.Cevap
  4. D
    A celestial body that lacks a subterranean thermal vent cannot be designated as a Class-Alpha hazard.
  5. E
    Celestial bodies that emit anomalous radiation are generally more hazardous than those harboring extremophile bacteria.

Cevap

Any celestial body that does not feature a crystalline core cannot be designated as a Class-Alpha hazard.
The correct answer accurately states the contrapositive of the synthesized logical chain. The stimulus establishes that a Class-Alpha hazard requires either extremophile bacteria or anomalous radiation. Because both of these possibilities independently mandate the presence of a stable magnetosphere, any Class-Alpha hazard must possess a stable magnetosphere. The final sentence establishes that a stable magnetosphere requires a crystalline core. Thus, any Class-Alpha hazard must feature a crystalline core. Taking the contrapositive of this relationship yields: if a celestial body lacks a crystalline core, it cannot be a Class-Alpha hazard.

Adım Adım Çözüm

1
Diagram the initial classification rule.
Class-Alpha Hazard (CAH) → Extremophile Bacteria (EB) OR Anomalous Radiation (AR).
The indicator phrase 'only if' introduces a necessary condition, which in this case is a compound 'or' statement.
2
Diagram the extremophile bacteria condition.
Extremophile Bacteria (EB) → Stable Magnetosphere (SM).
The phrasing 'No X without Y' translates directly to 'If X, then Y' (or mathematically, ~Y → ~X, which contraposes to X → Y).
3
Diagram the anomalous radiation conditions.
Anomalous Radiation (AR) → Thermal Vent (STV) → Stable Magnetosphere (SM). Therefore, AR → SM.
'Requires' introduces a necessary condition, and 'any' introduces a sufficient condition. Both statements chain together directly to SM.
4
Synthesize the branches.
Class-Alpha Hazard (CAH) → Stable Magnetosphere (SM).
Because CAH requires either EB or AR, and BOTH of those conditions independently require SM, it is guaranteed that CAH requires SM.
5
Diagram the final condition and form the contrapositive.
Stable Magnetosphere (SM) → Crystalline Core (CC). The full chain is CAH → CC. Contrapositive: ~CC → ~CAH.
'Unless X, cannot Y' means 'If Y, then X'. Connecting this to our synthesis yields CAH → SM → CC. Negating and reversing the ends provides the valid deduction.

Anahtar Kavram

Synthesizing conditional chains involving disjunctions and deriving the valid contrapositive of a multi-step deduction.
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Konular

Diagramming Conditional Statements

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