Examkin

Question

Difficulty: MediumParallel Valid Structure

Identify the precise formal logical framework that accurately characterizes the deductive reasoning employed in each practical scenario below.

  • If the deep-sea submersible's pressure seal is compromised, its internal diagnostic light flashes red. The internal diagnostic light is not flashing red. Therefore, the pressure seal is not compromised.Denying the necessary condition to conclude that the sufficient condition has not been met.
  • The main stage must be illuminated by either the overhead floodlights or the floor-level spotlights. The overhead floodlights have lost power. Thus, the stage must be illuminated by the floor-level spotlights.Eliminating one of two available alternatives to establish that the remaining alternative must be true.
  • If the sourdough is left at room temperature for over twelve hours, it will over-proof. If the dough over-proofs, the baked loaf will have an overly dense texture. So, leaving the sourdough at room temperature for over twelve hours ensures the baked loaf will have an overly dense texture.Linking two conditional statements through a shared term to deduce a new overarching conditional relationship.
  • Every main-sequence star fuses hydrogen into helium in its core. The celestial body Sirius A is a main-sequence star. Hence, Sirius A fuses hydrogen into helium in its core.Applying a characteristic shared by all members of a specific category to an individual member of that category.

Answer

The submersible argument correctly matches denying the necessary condition. The stage lighting argument matches eliminating an alternative. The sourdough argument matches linking two conditional statements. The star argument matches applying a categorical characteristic to an individual.
Each practical scenario maps to exactly one fundamental valid deductive architecture. The submersible argument follows Modus Tollens (If A -> B. ~B. Therefore, ~A). The stage lighting argument follows Disjunctive Syllogism (A or B. ~A. Therefore, B). The sourdough argument follows Chain Conditionals (If A -> B, If B -> C. Therefore, If A -> C). The astrophysics argument follows Universal Instantiation (All A are B. X is A. Therefore, X is B).

Step-by-Step Solution

1
Analyze the underlying structural components of the submersible argument.
The structure establishes an if-then premise, notes the 'then' outcome did not happen, and concludes the 'if' condition did not happen.
This isolates the formal valid deduction pattern known as Modus Tollens (denying the necessary condition).
2
Analyze the underlying structural components of the stage lighting argument.
The structure presents two mutually exclusive requirements, removes the first, and concludes the second must be true.
This identifies the pattern of Disjunctive Syllogism (eliminating an alternative).
3
Analyze the underlying structural components of the sourdough argument.
The structure introduces a condition leading to a middle outcome, which in turn leads to a final outcome, linking the very first condition to the very last outcome.
This demonstrates a Chain of Conditionals, also known as Hypothetical Syllogism.
4
Analyze the underlying structural components of the main-sequence star argument.
The structure provides a universal rule for an entire group and identifies a specific entity within that group, concluding the rule applies to the entity.
This matches the classic logical structure of Universal Instantiation.

Key Concept

Parallel Valid Structure
Rate this question

Topics

Parallel Valid Structure

More questions from this topic