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Difficulty: HardQuantifier Logic (Some, Most, All)

A comprehensive survey of flora in the Veridia Valley documented various characteristics of the local plant species. Every plant species in the valley that produces nectar is pollinated by indigenous insects. Most of the valley's plant species that are pollinated by indigenous insects flower during the early spring. In addition, some of the plant species in the valley that produce nectar are classified as toxic to mammals.

Which one of the following must be true based on the information provided?

  1. At least some of the plant species in the valley that are toxic to mammals are pollinated by indigenous insects.Answer
  2. B
    Most of the plant species in the valley that produce nectar flower during the early spring.
  3. C
    At least some of the plant species in the valley that are toxic to mammals flower during the early spring.
  4. D
    Most of the plant species in the valley that are toxic to mammals produce nectar.
  5. E
    Any plant species in the valley that is pollinated by indigenous insects also produces nectar.

Answer

At least some of the plant species in the valley that are toxic to mammals are pollinated by indigenous insects.
The correct answer follows strictly from the first and third premises. The third premise establishes that there is an intersection between nectar-producing plants and toxic plants (i.e., there are plants that are both). The first premise establishes a universal rule: every single nectar-producing plant is pollinated by insects. Applying this universal rule to the intersection, those specific toxic, nectar-producing plants must also be pollinated by insects. Therefore, it is absolutely true that some toxic plants are pollinated by insects.

Step-by-Step Solution

1
Translate the statements into formal logical relationships.
Statement 1: All Nectar -> Pollinated by Insects. Statement 2: Most Pollinated by Insects -> Flower in Spring. Statement 3: Some Nectar -> Toxic to Mammals.
Mapping the quantifiers allows us to see how the groups interact without being distracted by the subject matter.
2
Identify connections between the 'Some' statement and the 'All' statement.
We know that at least one plant is both Nectar-producing and Toxic (from Statement 3). We also know that every single Nectar-producing plant is Pollinated by Insects (from Statement 1).
The most reliable valid deductions in quantifier logic come from combining 'Some' statements with 'All' statements.
3
Derive the logically guaranteed conclusion.
Since the toxic, nectar-producing plants mentioned in Statement 3 must follow the rule established in Statement 1, they must be pollinated by insects. Therefore, at least some toxic plants are pollinated by insects.
If an entity possesses trait X (Nectar), and ALL things with trait X have trait Y (Pollinated by Insects), then that specific entity must also have trait Y.

Key Concept

Quantifier Logic (Some, Most, All)
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Topics

Quantifier Logic (Some, Most, All)

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