{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-quantifier"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-quantifier-01","title":{"zh-Hant":"量詞與明示論域：在有限整數論域上判定全稱、存在及其否定","en":"Quantifiers and explicit domains: deciding universal and existential statements and their negations on a finite integer domain"},"summary":{"zh-Hant":"在明示有限論域 U={−2,−1,0,1,2,3} 上，判定 φ₁：∀x∈U, x²<10；φ₂：∀x∈U, x²>x；φ₃：∃x∈U, x²=2 的真假；正確寫出 φ₂ 與 φ₃ 的否定；並說明論域為空集合時全稱與存在陳述的真假。","en":"On the explicit finite domain U={−2,−1,0,1,2,3}, decide the truth of φ₁: ∀x∈U, x²<10; φ₂: ∀x∈U, x²>x; φ₃: ∃x∈U, x²=2; write the negations of φ₂ and φ₃ correctly; and settle the truth of universal and existential statements when the domain is the empty set."},"mko_ids":["mko-quantifier"]}],"title":"Concept derivation guides"}