Syllogism — Files, numbered, and coded (ambiguity check): Statements: • Some files are numbered. • All numbers are coded. Which inference necessarily follows?

Introduction / Context:
This question is intentionally tricky because the middle term shifts in sense. The first premise talks about “numbered (files)”; the second talks about “numbers” (as entities). Without a valid middle-term link, no conclusion about files and coding is forced.

Given Data / Assumptions:

• Premise 1: Some files are numbered (∃ File that possess the property “numbered”).
• Premise 2: All numbers are coded (Number ⊆ Coded).
• No explicit link between “numbered (as a property of files)” and the noun class “numbers.”

Concept / Approach:
In syllogisms, the middle term must be used in the same sense. Here, “numbered” (adjective on files) is not the same as the noun class “numbers.” Thus, we cannot lawfully chain the premises.

Step-by-Step Evaluation of Options:
(a) “All files are coded” is an illicit generalization.(b) “All codes are filed” reverses and alters classes.(c) “Some files are not numbered” might be true, but it is not necessary from the premises; the first premise allows the rest of files to be numbered or not.(d) “No numbers have codes” contradicts Premise 2.

Verification / Alternative check:
A model where some files are numbered, numbers are coded, but no statement connects numbered-files to “coded” validates that none of (a)–(d) must hold.

Final Answer:
None of these.