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Zorluk: OrtaMust Be True / Most Strongly Supported

Archaeologists analyzing Bronze Age metallurgy across Aegean excavation sites have established the following:

Every Aegean bronze artifact with a tin concentration exceeding 12 percent by weight was forged using cassiterite ore sourced from the Anatolian plateau.
Any artifact forged using Anatolian cassiterite ore contains detectable trace amounts of the isotope lead-208.
Several excavated ceremonial daggers from the settlement of Akrotiri are Aegean bronze artifacts that do not contain detectable trace amounts of lead-208.

If the statements above are true, which one of the following must also be true?

  1. A
    Every Aegean bronze artifact that contains detectable trace amounts of lead-208 has a tin concentration exceeding 12 percent by weight.
  2. B
    None of the ceremonial daggers excavated from the settlement of Akrotiri were forged using cassiterite ore sourced from the Anatolian plateau.
  3. At least some of the ceremonial daggers excavated from Akrotiri do not have a tin concentration exceeding 12 percent by weight.Cevap
  4. D
    Any Aegean bronze artifact forged without Anatolian cassiterite ore contains no detectable lead isotopes of any kind.
  5. E
    Cassiterite ore from sources other than the Anatolian plateau typically produces bronze with lower overall durability than ore from Anatolia.

Cevap

At least some of the ceremonial daggers excavated from Akrotiri do not have a tin concentration exceeding 12 percent by weight.
The stimulus establishes a conditional chain: if an Aegean bronze artifact has a tin concentration exceeding 12 percent, it was forged using Anatolian cassiterite, which in turn guarantees the presence of lead-208. The contrapositive dictates that if an Aegean bronze artifact lacks detectable lead-208, its tin concentration cannot exceed 12 percent. Because several ceremonial daggers from Akrotiri are Aegean bronze artifacts lacking lead-208, it strictly must be true that at least some ceremonial daggers from Akrotiri do not have a tin concentration exceeding 12 percent by weight.

Adım Adım Çözüm

1
Diagram the formal conditional relationship provided in the premises.
Tin concentration > 12% → Anatolian cassiterite → Lead-208 present.
Connecting the two universal conditional statements forms a transitive chain linking high tin concentration to the presence of lead-208.
2
Derive the contrapositive of the combined conditional chain.
No Lead-208 → Not Anatolian cassiterite → Tin concentration ≤ 12%.
A conditional statement is logically equivalent to its contrapositive.
3
Apply the contrapositive deduction to the factual quantifier premise about Akrotiri daggers.
Since several Akrotiri daggers lack lead-208, those specific daggers must have a tin concentration that does not exceed 12 percent by weight.
An existential fact ('several' / 'some') combined with a valid conditional deduction guarantees that those particular items satisfy the necessary condition.

Anahtar Kavram

Deductive Conditional Chaining and Contraposition with Quantifiers
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Konular

Must Be True / Most Strongly Supported

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