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Difficulty: MediumChaining Conditional Statements

If the proposed highway expansion is approved, the adjacent wetlands will be drained. The wetlands will be drained only if the local wildlife council's objections are overruled. Furthermore, any drainage of the wetlands will result in a decline in the migratory bird population, and a decline in this population always leads to a drop in eco-tourism revenue.

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

  1. A
    If local eco-tourism revenue drops, then the proposed highway expansion must have been approved.
  2. B
    If the proposed highway expansion is not approved, then local eco-tourism revenue will not drop.
  3. If local eco-tourism revenue does not drop, then the proposed highway expansion was not approved.Answer
  4. D
    If the local wildlife council's objections are overruled, the migratory bird population will decline.
  5. E
    The local wildlife council's objections are motivated by a desire to protect eco-tourism revenue.

Answer

If local eco-tourism revenue does not drop, then the proposed highway expansion was not approved.
The stimulus establishes a direct sequence of conditional statements: Highway Approved -> Wetlands Drained -> Bird Decline -> Revenue Drop. The valid contrapositive of this entire sequence is: No Revenue Drop -> Highway Not Approved. The correct answer precisely states this logically guaranteed outcome.

Step-by-Step Solution

1
Formalize the conditional statements presented in the stimulus.
1. Highway Approved -> Wetlands Drained
2. Wetlands Drained -> Objections Overruled
3. Wetlands Drained -> Bird Decline
4. Bird Decline -> Revenue Drop
Translating English statements into formal logical notation reveals their precise relationships.
2
Identify the primary conditional chain that connects the majority of the variables.
Highway Approved -> Wetlands Drained -> Bird Decline -> Revenue Drop
Chaining allows us to see the ultimate necessary outcomes of the initial sufficient trigger.
3
Determine the valid contrapositive of the combined conditional chain.
No Revenue Drop -> No Bird Decline -> No Wetlands Drained -> Highway Not Approved
In 'Must Be True' formal logic questions, the correct answer is frequently the contrapositive of the main logical chain.

Key Concept

Chaining Conditional Statements
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Topics

Chaining Conditional Statements

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