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Question

Difficulty: HardSufficient Assumption

Consider the following argument:

Only algorithms that undergo rigorous adversarial testing can successfully identify zero-day vulnerabilities. Furthermore, if an algorithmic system requires massive computational overhead, it cannot be deployed on edge devices. The newly developed 'Aegis' protocol is capable of identifying zero-day vulnerabilities. Therefore, the 'Aegis' protocol cannot be deployed on edge devices.

Statement: The assumption "Any algorithmic system that does not require massive computational overhead has not undergone rigorous adversarial testing" is sufficient to logically guarantee the argument's conclusion.

Answer: Answer

Answer

True
The statement accurately identifies a sufficient assumption. The required logical bridge is 'Rigorous Testing →\rightarrow Massive Overhead'. The provided assumption is its valid contrapositive ('∼\sim Massive Overhead →\rightarrow ∼\sim Rigorous Testing'), which perfectly completes the deductive chain and guarantees the conclusion.

Step-by-Step Solution

1
Map the formal logic of the premises.
Identify Zero-Day →\rightarrow Rigorous Testing. Massive Overhead →\rightarrow Cannot Deploy on Edge. Aegis →\rightarrow Identify Zero-Day.
Translating the text into conditional relationships is necessary to find the structural gap in the argument.
2
Identify the conclusion and trace the existing logical chain.
Conclusion: Aegis →\rightarrow Cannot Deploy on Edge. Current chain: Aegis →\rightarrow Identify Zero-Day →\rightarrow Rigorous Testing.
This establishes what is known and what needs to be proven deductively.
3
Determine the required missing link.
We need to connect 'Rigorous Testing' to 'Cannot Deploy on Edge'. Since 'Massive Overhead' leads to 'Cannot Deploy on Edge', the required bridge is: Rigorous Testing →\rightarrow Massive Overhead.
A sufficient assumption must fill the exact deductive gap to guarantee the conclusion.
4
Evaluate the provided assumption against the required missing link.
The provided assumption is: Does not require massive overhead →\rightarrow Has not undergone rigorous testing (∼\sim Massive Overhead →\rightarrow ∼\sim Rigorous Testing). This is the logically equivalent contrapositive of the required bridge (Rigorous Testing →\rightarrow Massive Overhead).
A contrapositive functions identically to the original conditional statement, making the assumption completely sufficient.

Key Concept

Sufficient assumptions must provide absolute logical validity to the conclusion by supplying a missing deductive link. This missing link can be presented in its contrapositive form and remain entirely valid.
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Topics

Sufficient Assumption

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