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Difficulty: MediumDiagramming Conditional Statements

According to the newly revised deep-sea exploration safety protocols, a submersible is certified for trench operations only if its hull is constructed using a titanium-carbon matrix. Unless a vessel has an upgraded pressure-compensation system, it cannot be constructed using a titanium-carbon matrix. An upgraded pressure-compensation system is never approved for installation without the vessel passing an acoustic integrity scan. Furthermore, passing the acoustic integrity scan requires the installation of redundant hydrostatic sensors.

Based on the safety protocols described above, which of the following must be true?

  1. Any submersible that does not have redundant hydrostatic sensors installed is not certified for trench operations.Answer
  2. B
    If a submersible passes the acoustic integrity scan, its hull is constructed using a titanium-carbon matrix.
  3. C
    Any submersible that lacks a titanium-carbon matrix hull does not have redundant hydrostatic sensors installed.
  4. D
    Installing redundant hydrostatic sensors is sufficient to guarantee that a submersible will pass the acoustic integrity scan.
  5. E
    Titanium-carbon matrix hulls provide the greatest protection against structural failure during extreme depth operations.

Answer

Any submersible that does not have redundant hydrostatic sensors installed is not certified for trench operations.
The correct answer accurately reflects the contrapositive of the entire conditional chain. The stimulus establishes that certification requires a titanium hull (C -> T), which requires an upgraded system (T -> U), which requires an acoustic scan (U -> S), which in turn requires redundant sensors (S -> R). By linking these, we get: Certification -> Redundant sensors (C -> R). The contrapositive of this relationship is: No redundant sensors -> No certification (~R -> ~C).

Step-by-Step Solution

1
Identify and translate the first conditional relationship.
Certified for trench operations (C) -> Titanium-carbon matrix hull (T).
The phrase 'only if' introduces a necessary condition.
2
Translate the second and third conditional relationships.
Titanium-carbon matrix hull (T) -> Upgraded pressure-compensation system (U). Upgraded system (U) -> Acoustic integrity scan (S).
The phrase 'unless' means 'if not', creating the conditional: If not U, then not T (which translates to T -> U). The phrase 'never... without' also creates a necessary condition: U -> S.
3
Translate the final conditional relationship and combine all statements into a chain.
Scan (S) -> Redundant sensors (R). The full chain is: C -> T -> U -> S -> R.
The word 'requires' indicates a necessary condition. Connecting the shared terms creates the full logical progression.
4
Form the contrapositive of the entire chain to find the correct valid deduction.
If not R -> not S -> not U -> not T -> not C. Therefore, lacking redundant sensors means the submersible is not certified.
Correct answers in conditional chain questions often rely on the contrapositive of the relationship between the first and last terms.

Key Concept

Diagramming Conditional Statements and Forming Deductive Chains
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Topics

Diagramming Conditional Statements

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