DAG ⇔ Topological Order (∃ strict total order ∀ edges)

Prompt (Question • Data • Logic)

Question.
Is the directed graph G=(V,E) a DAG?
Data.
V = {a,b,c,d,e}   E = { a→b, a→c, b→d, c→d, d→e }
Logic (Second-Order).
∃ < ⊆ V×V. StrictTotalOrder(<) ∧ ∀(u→v)∈E. u < v
This quantifies over the binary relation “<” (a topological order), which is second-order.

Answer

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Reason Why

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Checks (at least 5)

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Diagnostics

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