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Zorluk: Çok zorChaining Conditional Statements

A deep-sea research station operates under strict automated environmental control protocols. Match each set of protocol conditions (Left) with the logically valid deduction that MUST be true based on those conditions (Right).

  • Protocol 1: Ventilation Unit A's activation is sufficient to isolate Sector B. Sector G's activation is a necessary condition for Sector D to pressurize. However, Sector G cannot activate if Sector B is isolated.If Sector D pressurizes, then Ventilation Unit A cannot be active.
  • Protocol 2: Filter E is purged unless Valve Z is secured. Manifold H failing precludes Valve Z from being secured. Furthermore, Pump T activating requires that Filter E not be purged.If Pump T activates, it must be the case that Manifold H has not failed.
  • Protocol 3: Generator I synchronizes if, and only if, Turbine K delays. Diagnostic L verifying depends on Generator I synchronizing. Relay M going offline is a necessary consequence of Turbine K delaying.Relay M failing to go offline guarantees that Diagnostic L does not verify.
  • Protocol 4: Module N is sealed when, and only when, Hatch X is unlatched. Override O being engaged is sufficient to seal Module N. Sensor P's activation guarantees that Hatch X is latched.Sensor P activating ensures that Override O is not engaged.

Cevap

Protocol 1 matches with the deduction about Sector D and Unit A. Protocol 2 matches with the deduction about Pump T and Manifold H. Protocol 3 matches with the deduction about Relay M and Diagnostic L. Protocol 4 matches with the deduction about Sensor P and Override O.
Each correct pairing represents a flawless deductive chain formed by translating advanced conditional indicators (sufficient, necessary, unless, requires, precludes) into formal logic, finding the linkages, and tracing the contrapositive path to an unavoidable conclusion.

Adım Adım Çözüm

1
Translate Protocol 1 into formal logic and chain the conditions.
A -> B; D -> G; B -> ~G. Chaining yields D -> G -> ~B -> ~A.
This establishes that if D pressurizes, A must be inactive, confirming the match.
2
Translate Protocol 2 into formal logic and chain the conditions.
The 'unless' statement becomes ~Z -> E (or ~E -> Z). 'Precludes' means H -> ~Z. 'Requires' means T -> ~E. Chaining yields T -> ~E -> Z -> ~H.
This proves that activating T guarantees H has not failed.
3
Translate Protocol 3 into formal logic and chain the conditions.
I <-> K; L -> I; K -> M. Forward chain: L -> I -> K -> M. Contrapositive chain: ~M -> ~K -> ~I -> ~L.
This confirms that if Relay M fails to go offline (~M), Diagnostic L does not verify (~L).
4
Translate Protocol 4 into formal logic and chain the conditions.
N <-> X_unlatched; O -> N; P -> X_latched (which is ~X_unlatched). Chain: P -> ~X_unlatched -> ~N -> ~O.
This proves that Sensor P activating guarantees Override O is not engaged.

Anahtar Kavram

Chaining Conditional Statements through advanced linguistic triggers and contrapositives.
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