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Zorluk: ZorSufficient Assumption

An archaeologist analyzes ceramic production methods across ancient regional settlements and constructs the following deductive argument. Which terms correctly fill in the blanks to complete the sufficient assumption that makes the conclusion follow with absolute logical certainty?

Cevap:Premise 1: Any ceramic vessel containing high scandium concentrations was fired in kilns fueled exclusively by highland tamarack.
Premise 2: Any kiln fueled exclusively by highland tamarack is incapable of reaching temperatures exceeding 900 degrees Celsius.
Conclusion: Therefore, no ceramic vessel containing high scandium concentrations was produced in the lowland coastal workshops.

Sufficient Bridge: The conclusion follows logically if it is assumed that every ceramic vessel produced in the lowland coastal workshops was fired at a temperature 【above】 900 degrees Celsius, thereby precluding the use of 【highland tamarack】.

Cevap

The argument requires establishing that lowland coastal workshop vessels were fired at temperatures exceeding 900 degrees Celsius, which precludes the use of highland tamarack.
The premises establish that containing high scandium concentrations requires using highland tamarack (Scandium -> Tamarack), which in turn requires firing temperatures at or below 900°C (Tamarack -> <=900°C). By contrapositive, any ceramic fired at a temperature above 900°C cannot have used highland tamarack (>900°C -> Not Tamarack) and therefore cannot contain high scandium concentrations (Not Tamarack -> Not Scandium). Assuming that every vessel produced in lowland coastal workshops was fired above 900°C (precluding highland tamarack) deductively guarantees that no lowland coastal vessel contains high scandium concentrations.

Adım Adım Çözüm

1
Map the formal conditional relationships in the premises
Premise 1 yields 'Scandium implies Highland Tamarack'. Premise 2 yields 'Highland Tamarack implies Firing Temperature at most 900°C'. Combining these by transitivity yields 'Scandium implies Firing Temperature at most 900°C'.
Establishing the intermediate conditional chain is necessary to identify the scope of what scandium ceramics entail.
2
Take the contrapositive of the combined premises
Contrapositive: 'Firing Temperature exceeding 900°C implies No Highland Tamarack, which implies No Scandium'.
The conclusion claims that vessels from lowland coastal workshops contain no scandium; linking lowland workshops to a temperature above 900°C enables the contrapositive chain.
3
Identify the missing sufficient link to establish the conclusion
Assuming 'Lowland Coastal implies Firing Temperature above 900°C' guarantees that lowland ceramics could not use highland tamarack, thereby deductively guaranteeing that no lowland ceramic contains scandium.
A sufficient assumption must close the inferential gap 100% deductively: Lowland implies >900°C implies Not Highland Tamarack implies Not Scandium.

Anahtar Kavram

Sufficient Assumption via Contrapositive Conditional Linkage
Tahmini Süre:1m 30s
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Sufficient Assumption

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