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Zorluk: ZorMust Be True / Most Strongly Supported

Marine geochemists and oceanographers surveying benthic hydrothermal fields have established the following facts regarding deep-sea vent systems:

• Any hydrothermal site that hosts hyperthermophilic methanogen colonies exhibits sub-seafloor serpentinization.
• No site exhibiting sub-seafloor serpentinization possesses basalt crust younger than one million years.
• Every hydrothermal site possessing basalt crust of at least one million years is situated along an ultra-slow spreading ridge.
• Some hydrothermal sites situated along an ultra-slow spreading ridge generate diffuse, low-temperature venting rather than focused chimney discharge.
• Any hydrothermal site that generates diffuse, low-temperature venting is incapable of sustaining predatory siphonophore populations.

Which of the following statements must be true based on the oceanographers' findings? Select all that apply.

  1. Any hydrothermal site that hosts hyperthermophilic methanogen colonies is situated along an ultra-slow spreading ridge.Cevap
  2. B
    Every hydrothermal site that is situated along an ultra-slow spreading ridge exhibits sub-seafloor serpentinization.
  3. At least some hydrothermal sites situated along an ultra-slow spreading ridge are incapable of sustaining predatory siphonophore populations.Cevap
  4. D
    Any hydrothermal site that does not host hyperthermophilic methanogen colonies possesses basalt crust younger than one million years.
  5. E
    No hydrothermal site situated along an ultra-slow spreading ridge is capable of sustaining predatory siphonophore populations.

Cevap

The statements that must be true are the one establishing that any site hosting hyperthermophilic methanogen colonies is on an ultra-slow spreading ridge, and the one establishing that at least some sites along an ultra-slow spreading ridge cannot sustain predatory siphonophores.
The first valid statement directly follows from transitive conditional chaining: Methanogen colonies →\rightarrow Serpentinization →\rightarrow Basalt crust ≥1\ge 1 million years →\rightarrow Ultra-slow spreading ridge. The second valid statement follows from combining the existential premise (some ultra-slow ridge sites have diffuse venting) with the universal conditional rule (diffuse venting →\rightarrow cannot sustain siphonophores), which strictly proves that some ultra-slow ridge sites cannot sustain siphonophores.

Adım Adım Çözüm

1
Formalize the universal conditional statements from the stimulus into symbolic chains.
Methanogen colonies imply Serpentinization; Serpentinization implies Basalt crust ≥1\ge 1 million years; Basalt crust ≥1\ge 1 million years implies Ultra-slow spreading ridge. Diffuse venting implies No siphonophores.
Establishing explicit conditional linkages allows for valid chain deductions and contrapositives.
2
Synthesize the conditional chain from methanogen presence to ridge location.
Methanogen →\rightarrow Serpentinization →\rightarrow Crust ≥1\ge 1 million years →\rightarrow Ultra-slow ridge. Therefore, Methanogen →\rightarrow Ultra-slow ridge.
Transitivity of conditional relationships guarantees that any site hosting methanogens must be on an ultra-slow ridge.
3
Combine the existential quantifier statement with the dependent conditional rule.
There exist ultra-slow ridge sites with diffuse venting, and all diffuse venting sites lack siphonophores. Thus, some ultra-slow ridge sites cannot sustain siphonophores.
An existential statement combined with a universal rule governing the subgroup strictly proves an existential conclusion about that subgroup.
4
Evaluate and eliminate all invalid inferences.
Reversals, invalid negations, and unwarranted universal generalizations are discarded.
Only deductively guaranteed statements satisfy the standard for must be true questions.

Anahtar Kavram

Conditional Chaining and Quantifier Synthesis in Formal Deductive Logic
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Must Be True / Most Strongly Supported

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