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Difficulty: MediumChaining Conditional Statements

According to the newly implemented botanical garden regulations, if a botanical specimen is classified as a delicate cultivar, it must be kept in the restricted conservatory. A specimen can be kept in the restricted conservatory only if it undergoes weekly pathogen screening. Furthermore, any specimen that undergoes weekly pathogen screening is exempt from the standard public exhibition rotation.

Based on the regulations above, which of the following must be true?

  1. A
    If a botanical specimen is exempt from the standard public exhibition rotation, it is classified as a delicate cultivar.
  2. B
    If a botanical specimen is not classified as a delicate cultivar, it is part of the standard public exhibition rotation.
  3. If a botanical specimen is part of the standard public exhibition rotation, it is not classified as a delicate cultivar.Answer
  4. D
    If a botanical specimen undergoes weekly pathogen screening, it must be kept in the restricted conservatory.
  5. E
    Most specimens that are exempt from the standard public exhibition rotation are kept in the restricted conservatory.

Answer

If a botanical specimen is part of the standard public exhibition rotation, it is not classified as a delicate cultivar.
The premises create a continuous logical chain: being a delicate cultivar guarantees placement in the restricted conservatory, which guarantees pathogen screening, which guarantees exemption from the public exhibition rotation (Delicate Cultivar -> Not in Exhibition). The correct answer is the logical contrapositive of this final chain: if a specimen IS in the public exhibition rotation, it cannot be a delicate cultivar (In Exhibition -> Not a Delicate Cultivar).

Step-by-Step Solution

1
Translate the rules into conditional statements.
1: Delicate Cultivar (DC) -> Restricted Conservatory (RC). 2: Restricted Conservatory (RC) -> Weekly Pathogen Screening (WPS). 3: Weekly Pathogen Screening (WPS) -> Not in Public Exhibition Rotation (~PER).
Formalizing the logic makes it easier to track the relationships, noting that 'only if' introduces a necessary condition.
2
Chain the conditional statements together.
DC -> RC -> WPS -> ~PER.
Since the necessary condition of each rule matches the sufficient condition of the next, they can be linked into a continuous chain.
3
Derive valid inferences and their contrapositives.
Valid chain inference: DC -> ~PER. Contrapositive: PER -> ~DC.
The correct answer to a Must Be True question involving formal logic is almost always the chained conclusion or its direct contrapositive.

Key Concept

Chaining Conditional Statements
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Topics

Chaining Conditional Statements

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