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Zorluk: ZorMust Be True Questions

Under the revised international pharmacopeia standards, any commercially distributed sedative derived from the Valeriana plant must undergo a proprietary alkalinization process. Undergoing the proprietary alkalinization process requires the use of specialized titanium-lined reactors. None of the sedatives manufactured by the firm Botanica-Med use specialized titanium-lined reactors, although some of the sedatives manufactured by Botanica-Med are currently authorized for pediatric use.

Based strictly on the information above, the following statement must be true: At least one sedative currently authorized for pediatric use is not a commercially distributed sedative derived from the Valeriana plant.

Cevap: Cevap

Cevap

True
The statement is logically guaranteed by linking the contrapositive of the required conditions with the existence of Botanica-Med's pediatric sedatives.

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1
Diagram the conditional statements provided in the first two sentences.
Valeriana derivation → Alkalinization → Titanium reactors.
This establishes the necessary conditions for any commercially distributed sedative derived from the Valeriana plant.
2
Evaluate the information about Botanica-Med using the contrapositive of the logic chain.
Botanica-Med → NO Titanium reactors → NO Alkalinization → NOT a Valeriana derivation.
Since Botanica-Med products fail to meet a necessary condition (titanium reactors), they cannot possibly be Valeriana-derived sedatives.
3
Combine the deduction from Step 2 with the existential quantifier ('some') provided in the final sentence.
Some Botanica-Med sedatives are authorized for pediatric use. Since NO Botanica-Med sedatives are Valeriana derivations, some pediatric-authorized sedatives are NOT Valeriana derivations.
This proves the statement that at least one sedative currently authorized for pediatric use is not a commercially distributed sedative derived from the Valeriana plant.

Anahtar Kavram

Chaining conditional statements, forming contrapositives, and combining them with existential ('some') quantifiers to derive a guaranteed truth.
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