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Difficulty: HardForming Contrapositives

According to the newly ratified International Maritime Treaty, a sovereign vessel is permitted to navigate through the restricted ecological zone only if it possesses a valid ecological waiver or operates exclusively on electric power.

Which one of the following statements can be logically inferred from the treaty regulations above?

  1. A
    Any sovereign vessel that possesses a valid ecological waiver or operates exclusively on electric power is permitted to navigate through the restricted ecological zone.
  2. Any sovereign vessel that neither possesses a valid ecological waiver nor operates exclusively on electric power is prohibited from navigating through the restricted ecological zone.Answer
  3. C
    Any sovereign vessel that is prohibited from navigating through the restricted ecological zone must lack a valid ecological waiver and fail to operate exclusively on electric power.
  4. D
    Any sovereign vessel that lacks a valid ecological waiver or fails to operate exclusively on electric power is prohibited from navigating through the restricted ecological zone.
  5. E
    Any sovereign vessel that operates exclusively on electric power is automatically granted a valid ecological waiver.

Answer

The logically valid inference is that a vessel lacking both a valid ecological waiver and electric power cannot navigate the restricted zone.
The correct answer accurately applies De Morgan's laws to form a valid contrapositive. The stimulus dictates that permission to navigate requires at least one of two things: a waiver OR electric power. Therefore, if a vessel lacks BOTH (neither a waiver nor electric power), it has failed the necessary condition and must be prohibited from navigating.

Step-by-Step Solution

1
Diagram the original conditional statement from the stimulus.
Permitted to Navigate -> (Possesses Waiver OR Operates on Electric Power)
The phrase 'only if' introduces a necessary condition. Because there are two ways to meet it, we use the logical 'OR'.
2
Form the contrapositive by reversing the conditions and negating both sides.
NOT (Possesses Waiver OR Operates on Electric Power) -> NOT Permitted to Navigate
A valid logical inference from a conditional statement is its exact contrapositive.
3
Apply De Morgan's laws to simplify the negated compound necessary condition.
(NOT Possesses Waiver AND NOT Operates on Electric Power) -> NOT Permitted to Navigate
Negating an 'OR' statement turns it into an 'AND' statement. In plain English, 'not A or B' becomes 'neither A nor B'.
4
Match the resulting logical statement to the correct answer choice.
The correct option states that any vessel that neither possesses a waiver nor operates on electric power is prohibited from navigating.
This choice perfectly aligns with the simplified contrapositive diagram.

Key Concept

Forming compound contrapositives using De Morgan's laws (negating 'OR' into 'AND').
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Topics

Forming Contrapositives

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