// Numbas version: exam_results_page_options
{"name": "Relationen und deren Eigenschaften", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Relationen und deren Eigenschaften", "tags": [], "metadata": {"description": "<p>Untersuchung von Relationen</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Auf $\\mathbb{N}\\times\\mathbb{N}$ betrachten wir&nbsp;zwei Relationen $x\\mathbf{R}y$, deren Graphen im Bereich $x,y\\leq 12$&nbsp;so ausschauen:</p>\n<p><em><strong>Beachten Sie:</strong> Anders als auf den Folien ist hier $x\\mathbf{R}y$ und <strong>nicht</strong> $y\\mathbf{R}x$&nbsp; dargestellt. <br/>Bitte etwas Geduld beim Laden der Graphen.</em></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">\n<h4>&nbsp;A</h4>\n</td>\n<td style=\"text-align: center;\">\n<h4>&nbsp;B</h4>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">{apps[0]}</td>\n<td style=\"text-align: center;\">{apps[1]}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>Zu Aufgabenteil a): </strong></p>\n<p>Die L&ouml;sung findet man durch &Uuml;berpr&uuml;fen der Werte einzelner Zahlenpaare $(x\\mid y)$, die in der Relation enthalten sein sollten oder nicht und bei denen man dann schaut, ob die entsprechenden Punkte in den Graphen enthalten sind oder nicht.</p>\n<p><strong>Zu Aufgabenteil b):</strong></p>\n<p><em>(i) Reflexivit&auml;t:</em></p>\n<p>reflexiv: Alle Punkte der Diagonalen m&uuml;ssen markiert sein.</p>\n<p>irreflexiv: Kein Punkt der Diagonalen darf markiert sein.</p>\n<p>weder reflexiv, noch irreflexiv: es gibt Punkte auf der Diagonalen, die markiert sind und solche, wo das nicht der Fall ist.</p>\n<p><em>(ii) Symmetrie</em></p>\n<p>symmetrisch:&nbsp;Alle Punkte auf oder unterhalb von $y=x$ haben Spiegelunkte an $y=x$ auf oder unterhalb der Geraden (und umgekehrt).</p>\n<p>antisymmetrisch: Das stimmt zwar nicht, aber&nbsp;alle Punkte auf der Geraden $y=x$ sind markiert.</p>\n<p>asymmetrisch:&nbsp;selbst&nbsp;das, was bei antisymmetrisch steht, ist nicht richtig.</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"a": {"name": "a", "group": "Listen", "definition": "distinct(a1+a2)", "description": "", "templateType": "anything"}, "Auswahl": {"name": "Auswahl", "group": "Relationen", "definition": "[\"gcd(x[0],x[1])<=\"+n,\"lcm(x[0],x[1])>=\"+m,\"mod(2*x[0]+3*x[1],\"+n+\")=mod(2*x[1]+3*x[0],\"+m+\")\",\"gcd(x[0],x[1])<>x[0]\",\"lcm(x[0],x[1])<x[0]*x[1]\",\"mod(x[0]-x[1],\"+n+\")=mod(x[1]-x[0],\"+n+\")\"]", "description": "", "templateType": "anything"}, "Graphs": {"name": "Graphs", "group": "Listen", "definition": "[filter(eval(expression(what[0])),x,a),filter(eval(expression(what[1])),x,a)]", "description": "", "templateType": "anything"}, "rando": {"name": "rando", "group": "Parameter", "definition": 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(A, B) jeweils&nbsp;die zugeh&ouml;rige&nbsp;Definition der Relation an (es gibt genau zwei richtige Antworten)!</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": "0", "maxAnswers": "2", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "checkbox", "warningType": "prevent", "showCellAnswerState": true, "choices": ["$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[0]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[1]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[2]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[3]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[4]])}", "$x{\\mathbf{R}}y :\\Leftrightarrow$ {latex(Auswahltex[rando[5]])}"], "matrix": [["2", "-1"], ["-1", "2"], ["-1", "-1"], ["-1", "-1"], ["-1", "-1"], ["-1", "-1"]], "layout": {"type": "all", "expression": ""}, "answers": ["Graph A", "Graph B"]}, {"type": "gapfill", "useCustomName": true, "customName": "Eigenschaften 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