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Question

Difficulty: MediumSufficient Assumption

An architectural acoustician constructs a deductive argument evaluating a newly designed performance venue. Complete the argument by identifying the missing premise that guarantees the conclusion follows logically and necessarily.

Answer:Premise 1: Any performance venue with an unbuffered resonance frequency below 120 Hz produces low-frequency standing waves.
Premise 2: Every performance venue that produces low-frequency standing waves is unsuitable for recording vocal polyphony.
Missing Premise: The Lyceum Auditorium 【has an unbuffered resonance frequency below 120 Hz】.
Conclusion: Therefore, the Lyceum Auditorium is unsuitable for recording vocal polyphony.

Answer

has an unbuffered resonance frequency below 120 Hz
Establishing that the Lyceum Auditorium has an unbuffered resonance frequency below 120 Hz triggers the full conditional chain (Resonance < 120 Hz → Standing Waves → Unsuitable for Vocal Polyphony), thereby deductively guaranteeing the conclusion with 100% logical certainty.

Step-by-Step Solution

1
Analyze the formal structure of the explicit premises and the conclusion.
Premise 1 establishes: Unbuffered resonance below 120 Hz → Low-frequency standing waves. Premise 2 establishes: Low-frequency standing waves → Unsuitable for vocal polyphony. The conclusion states: Lyceum Auditorium → Unsuitable for vocal polyphony.
Deconstructing the argument into conditional terms isolates the chain of deduction already established by the speaker.
2
Combine the premises to establish the overarching conditional rule.
By hypothetical syllogism: Unbuffered resonance below 120 Hz → Unsuitable for vocal polyphony.
Linking the two premises reveals the sufficient condition required to trigger the final necessary outcome.
3
Identify the deductive bridge required to reach the conclusion regarding the Lyceum Auditorium.
To reach the conclusion that the Lyceum Auditorium is unsuitable for recording vocal polyphony via modus ponens, the Lyceum Auditorium must satisfy the antecedent of the chain: it must have an unbuffered resonance frequency below 120 Hz.
A sufficient assumption must provide a 100% deductive guarantee of the conclusion when added to the existing premises.

Key Concept

Sufficient Assumption Deductive Chain Linking
Estimated Time:1m 15s
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Topics

Sufficient Assumption

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