{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","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-relation"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-relation-01","title":{"zh-Hant":"二元關係：定義域、關係像與逆關係的逐步計算","en":"Binary relations: computing the domain, images and the converse step by step"},"summary":{"zh-Hant":"設 A={1,2,3,4}、B={2,3,4,5,6}、R={(1,2),(1,3),(3,3),(4,6)}、C={1,3}。核對 R⊆A×B；計算 Dom(R)、R[C]、R[∅]、R⁻¹ 與 Dom(R⁻¹)；判定 R 是否為函數 A→B、R⁻¹ 是否為函數 B→A。","en":"Let A={1,2,3,4}, B={2,3,4,5,6}, R={(1,2),(1,3),(3,3),(4,6)} and C={1,3}. Check R⊆A×B; compute Dom(R), R[C], R[∅], R⁻¹ and Dom(R⁻¹); decide whether R is a function A→B and whether R⁻¹ is a function B→A."},"mko_ids":["mko-relation"]}],"title":"概念推導導讀"}