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Question

Difficulty: EasyConditional Logic and Formal Deductions

An agricultural board rule dictates that an orchard receives an organic certification only if it refrains from using synthetic pesticides for at least three consecutive years. Orchard Y has not used synthetic pesticides for the past four consecutive years.

Statement: Based on the rule above, Orchard Y must have received an organic certification.

Answer: Answer

Answer

The statement is False. Meeting a necessary condition does not guarantee that a sufficient condition is met.
The statement is False because the agricultural board rule uses the phrase 'only if', establishing that avoiding synthetic pesticides is a necessary requirement for certification, not a guarantee of it. Satisfying a necessary condition does not prove that the final outcome must occur.

Step-by-Step Solution

1
Identify the conditional relationship in the premise
Organic Certification → No synthetic pesticides for at least 3 years
The indicator 'only if' introduces a necessary condition.
2
Analyze the given fact about Orchard Y
Orchard Y satisfies the necessary condition (4 years without synthetic pesticides ≥ 3 years).
The premise states Orchard Y met the required timeframe.
3
Evaluate whether the conclusion logically follows
Inferring that Orchard Y must be certified is an invalid deduction (Mistaken Reversal).
Satisfying a necessary condition does not automatically trigger the outcome, as additional unstated conditions may be required.

Key Concept

Distinguishing Necessary Conditions from Sufficient Conditions
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Topics

Conditional Logic and Formal Deductions

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