Examkin

Soru

Zorluk: OrtaMust Be True / Most Strongly Supported

Ecologists studying alpine plant communities in the Cascade Range recorded the following observations regarding high-altitude perennial species:

• Every perennial species that produces anthocyanin-rich floral pigments possesses cellular cold-shock proteins.
• Any species possessing cellular cold-shock proteins is capable of surviving prolonged sub-zero temperatures without tissue necrosis.
• Some alpine perennial species that are pollinated exclusively by bumblebees produce anthocyanin-rich floral pigments.
• No species capable of surviving prolonged sub-zero temperatures without tissue necrosis exhibits early-spring dormancy.

Based on the ecologists' observations, which of the following statements must be true? (Select all that apply.)

  1. At least some alpine perennial species that are pollinated exclusively by bumblebees are capable of surviving prolonged sub-zero temperatures without tissue necrosis.Cevap
  2. B
    Any alpine perennial species capable of surviving prolonged sub-zero temperatures without tissue necrosis produces anthocyanin-rich floral pigments.
  3. No alpine perennial species that exhibits early-spring dormancy produces anthocyanin-rich floral pigments.Cevap
  4. D
    No alpine perennial species pollinated exclusively by bumblebees exhibits early-spring dormancy.
  5. E
    Possessing cellular cold-shock proteins is a necessary condition for an alpine perennial species to be pollinated exclusively by bumblebees.

Cevap

The statements that must be true are the one asserting that at least some bumblebee-pollinated alpine perennials can survive prolonged sub-zero temperatures without tissue necrosis, and the one stating that no species exhibiting early-spring dormancy produces anthocyanin-rich floral pigments.
The statements asserting sub-zero survival for some bumblebee-pollinated species and the absence of anthocyanin production in dormant species are deductively guaranteed. First, because some bumblebee-pollinated perennials produce anthocyanin, and all anthocyanin producers possess cold-shock proteins that confer sub-zero survival without necrosis, at least some bumblebee-pollinated perennials must possess this survival capacity. Second, the full conditional chain shows that every anthocyanin-producing species avoids early-spring dormancy; taking the contrapositive confirms that no species with early-spring dormancy can produce anthocyanin.

Adım Adım Çözüm

1
Formalize the conditional rules and quantifier relationships from the stimulus.
Anthocyanin →\rightarrow Cold-shock proteins →\rightarrow Sub-zero survival without necrosis →\rightarrow No early-spring dormancy. Additionally: Some Bumblebee-pollinated →\rightarrow Anthocyanin.
Translating premises into symbolic logic clarifies valid inferences, quantifier overlaps, and contrapositives.
2
Chain the quantifier premise through the conditional sequence.
Since some bumblebee-pollinated species produce anthocyanins, and all anthocyanin producers possess cold-shock proteins and survive sub-zero temperatures, there exist bumblebee-pollinated species with sub-zero survival capability.
An existential quantifier (Some XX are YY) combined with universal conditionals (Y→ZY \rightarrow Z) guarantees that Some XX are ZZ.
3
Derive the contrapositive of the full conditional chain.
The conditional chain Anthocyanin →\rightarrow No early-spring dormancy yields the contrapositive: Early-spring dormancy →\rightarrow No anthocyanin.
A conditional statement is logically equivalent to its contrapositive, establishing that any plant with early-spring dormancy cannot produce anthocyanins.

Anahtar Kavram

Conditional chaining, contrapositive derivation, and quantifier intersection in deductive logic
Tahmini Süre:1m 30s
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