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Zorluk: OrtaIdentifying Must-Be-True Statements and Valid Deductions

Under regional environmental regulation protocols, a coastal marine sanctuary receives Tier-1 Protection status if and only if it contains a documented coral spawning site and strictly prohibits all commercial fishing activities. Based on these regulations, evaluate the following statement:

A coastal marine sanctuary that lacks a documented coral spawning site cannot receive Tier-1 Protection status.

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Cevap

True. The statement is a valid deduction because a documented coral spawning site is a necessary condition for receiving Tier-1 Protection status.
The term 'if and only if' establishes a biconditional link, making a documented coral spawning site a strictly necessary condition for Tier-1 Protection status. Consequently, any sanctuary lacking such a site cannot meet the criteria for Tier-1 status, rendering the statement definitively True.

Adım Adım Çözüm

1
Analyze the conditional structure of the stimulus premise.
Tier-1 Status   ⟺  \iff (Documented Coral Spawning Site AND Commercial Fishing Prohibited).
The phrase 'if and only if' denotes a biconditional relationship where both components are mutually necessary and sufficient.
2
Evaluate the condition presented in the statement.
The sanctuary lacks a documented coral spawning site.
We need to test what happens when one of the necessary conditions is negated.
3
Deduce the logical outcome based on the premise.
Since a necessary condition is negated, Tier-1 Status cannot be achieved (¬Spawning Site  ⟹  ¬Tier-1 Status\neg\text{Spawning Site} \implies \neg\text{Tier-1 Status}).
Negating a necessary condition guarantees the negation of the outcome.

Anahtar Kavram

Necessary and sufficient conditions in biconditional logic statements
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Konular

Identifying Must-Be-True Statements and Valid Deductions

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