// Numbas version: exam_results_page_options
{"name": "Sets: Set logic", "extensions": ["geogebra"], "custom_part_types": [{"source": {"pk": 2, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/2/edit"}, "name": "List of numbers", "short_name": "list-of-numbers", "description": "<p>The answer is a comma-separated list of numbers.</p>\n<p>The list is marked correct if each number occurs the same number of times as in the expected answer, and no extra numbers are present.</p>\n<p>You can optionally treat the answer as a set, so the number of occurrences doesn't matter, only whether each number is included or not.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "join(\n  if(settings[\"correctAnswerFractions\"],\n    map(let([a,b],rational_approximation(x), string(a/b)),x,settings[\"correctAnswer\"])\n  ,\n    settings[\"correctAnswer\"]\n  ),\n  settings[\"separator\"] + \" \"\n)", "hint": {"static": false, "value": "if(settings[\"show_input_hint\"],\n  \"Enter a list of numbers separated by <code>{settings['separator']}</code>.\",\n  \"\"\n)"}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "bits:\nlet(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)\n\nexpected_numbers:\nlet(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)\n\nvalid_numbers:\nif(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )\n\nis_sorted:\nassert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )\n\nincluded:\nmap(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )\n\nall_included:\nall(included)\n\nno_extras:\nif(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )\n\ninterpreted_answer:\nif(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)\n\nmark:\nif(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)\n\nnotationStyles:\n[\"en\"]\n\nisSet:\nsettings[\"isSet\"]\n\nextra_numbers:\nfilter(not (x in expected_numbers),x,interpreted_answer)", "marking_notes": [{"name": "bits", "description": "<p>The separate items in the student's answer</p>", "definition": "let(b,filter(x<>\"\",x,split(studentAnswer,settings[\"separator\"])),\n    if(isSet,list(set(b)),b)\n)"}, {"name": "expected_numbers", "description": "", "definition": "let(l,settings[\"correctAnswer\"] as \"list\",\n    if(isSet,list(set(l)),l)\n)"}, {"name": "valid_numbers", "description": "<p>Is every number in the student's list valid?</p>", "definition": "if(all(map(not isnan(x),x,interpreted_answer)),\n    true,\n    let(index,filter(isnan(interpreted_answer[x]),x,0..len(interpreted_answer)-1)[0], wrong, bits[index],\n      warn(wrong+\" is not a valid number\");\n      fail(wrong+\" is not a valid number.\")\n    )\n  )"}, {"name": "is_sorted", "description": "<p>Are the student's answers in ascending order?</p>", "definition": "assert(sort(interpreted_answer)=interpreted_answer,\n    multiply_credit(0.5,\"Not in order\")\n  )"}, {"name": "included", "description": "<p>Is each number in the expected answer present in the student's list the correct number of times?</p>", "definition": "map(\n      let(\n        num_student,len(filter(x=y,y,interpreted_answer)),\n        num_expected,len(filter(x=y,y,expected_numbers)),\n        switch(\n          num_student=num_expected,\n            true,\n          num_student<num_expected,\n            incorrect(\n              if(isSet,\"Your answer does not contain \"+x+\" but should.\",\n                \"Your answer does not contain \"+x+\" enough times.\"\n              )\n            );false\n          ,\n            incorrect(\n              if(isSet,\"Your answer contains \"+x+\" but should not.\",\n                \"Your answer contains \"+x+\" too many times.\"\n              )\n            );false\n        )\n      )\n      ,\n      x,\n      sort(list(set(expected_numbers)))\n  )"}, {"name": "all_included", "description": "<p>Has every number been included the right number of times?</p>", "definition": "all(included)"}, {"name": "no_extras", "description": "<p>True if the student's list doesn't contain any numbers that aren't in the expected answer.</p>", "definition": "if(all(map(x in expected_numbers, x, interpreted_answer)),\n    true\n  ,\n    incorrect(\"Your answer contains \"+extra_numbers[0]+\" but should not.\");\n    false\n  )"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "if(lower(studentAnswer) in [\"empty\",\"\u2205\"],[],\n  map(\n    if(settings[\"allowFractions\"],parsenumber_or_fraction(x,notationStyles), parsenumber(x,notationStyles))\n    ,x\n    ,bits\n  )\n)"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=\"\",fail(\"You have not entered an answer\"),false);\napply(valid_numbers);\napply(included);\napply(no_extras);\ncorrectif(all_included and no_extras)"}, {"name": "notationStyles", "description": "", "definition": "[\"en\"]"}, {"name": "isSet", "description": "<p>Should the answer be considered as a set, so the number of times an element occurs doesn't matter?</p>", "definition": "settings[\"isSet\"]"}, {"name": "extra_numbers", "description": "<p>Numbers included in the student's answer that are not in the expected list.</p>", "definition": "filter(not (x in expected_numbers),x,interpreted_answer)"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The list of numbers that the student should enter. The order does not matter.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "allowFractions", "label": "Allow the student to enter fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "correctAnswerFractions", "label": "Display the correct answers as fractions?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": false}, {"name": "isSet", "label": "Is the answer a set?", "help_url": "", "hint": "If ticked, the number of times an element occurs doesn't matter, only whether it's included at all.", "input_type": "checkbox", "default_value": false}, {"name": "show_input_hint", "label": "Show the input hint?", "help_url": "", "hint": "", "input_type": "checkbox", "default_value": true}, {"name": "separator", "label": "Separator", "help_url": "", "hint": "The substring that should separate items in the student's list", "input_type": "string", "default_value": ",", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sets: Set logic", "tags": [], "metadata": {"description": "<p>Tests knowledge of union, intersection, subset, strict subset &amp; element of</p>", "licence": "None specified"}, "statement": "<p>Given that</p>\n<p>$\\var{n[0]} =\\var{Awrite}$&nbsp;</p>\n<p>and</p>\n<p>$\\var{n[1]} = \\var{Bwrite}$&nbsp;</p>", "advice": "<p><strong>part a)</strong></p>\n<p>$\\var{n[0]} \\cap \\var{n[1]}$ is read as 'the intersection of $\\var{n[0]}$ and $\\var{n[1]}$', which means 'the values that occur in both $\\var{n[0]}$ and $\\var{n[1]}$'.</p>\n<p><strong>part b)</strong></p>\n<p>$\\var{n[0]} \\cup \\var{n[1]}$ is read as 'the union of $\\var{n[0]}$ and $\\var{n[1]}$', which means 'the values that occur in either $\\var{n[0]}$ or $\\var{n[1]}$ or both'.</p>\n<p><strong>part c)</strong></p>\n<p>This question checks your understanding on the notation:</p>\n<ul>\n<li>$\\subset$ means \"is a proper subset of\" (i.e. each element of $\\var{n[0]}$ is contained within $\\var{n[1]}$ but the set $\\var{n[0]}$ is smaller than $\\var{n[1]}$)</li>\n<li>$\\subseteq$ means \"is a subset of\" (i.e. each element of $\\var{n[0]}$ is contained within $\\var{n[1]}$)</li>\n<li>$\\not \\subset$ means \"is not a subset of\"</li>\n<li>$\\not \\subseteq$ means \"is not a proper subset of\" (but it could be a subset of)</li>\n<li>$ \\in$ means \"is contained within\"</li>\n<li>$\\notin$ means \"is not contained within\"</li>\n</ul>\n<p></p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "distinct(sort(repeat(random(1..5),length[0])))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "distinct(sort(repeat(random(1..5),length[1])))", "description": "", "templateType": "anything", "can_override": false}, "justA": {"name": "justA", "group": "Ungrouped variables", "definition": "A except B", "description": "", "templateType": "anything", "can_override": false}, "justB": {"name": "justB", "group": "Ungrouped variables", "definition": "B except A\n", "description": "", "templateType": "anything", "can_override": false}, "AnB": {"name": "AnB", "group": "Ungrouped variables", "definition": "sort(AuB except justA except justB)\n", "description": "", "templateType": "anything", "can_override": false}, "AuB": {"name": "AuB", "group": "Ungrouped variables", "definition": "distinct(sort((A+B)))", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(['A','B'],['B','A'],['P','Q'],['Q','P'],['R','S'],['S', 'T'],['U','V'],['V','U'])", "description": "", "templateType": "anything", "can_override": false}, "AWrite": {"name": "AWrite", "group": "Ungrouped variables", "definition": "render(safe(\"{a}\"), [\"a\": A])", "description": "", "templateType": "anything", "can_override": false}, "length": {"name": "length", "group": "Ungrouped variables", "definition": "[random(2..5), random(2..5)]", "description": "", "templateType": "anything", "can_override": false}, "Bwrite": {"name": "Bwrite", "group": "Ungrouped variables", "definition": "render(safe(\"{a}\"), [\"a\": B])", "description": "", "templateType": "anything", "can_override": false}, "notAnB": {"name": "notAnB", "group": "Ungrouped variables", "definition": "sort(B except A)", "description": "", "templateType": "anything", "can_override": false}, "trueorfalse": {"name": "trueorfalse", "group": "Ungrouped variables", "definition": "[t1, t2, t3, t4, t5,t6] ", "description": "", "templateType": "anything", "can_override": false}, "trueorfalseans": {"name": "trueorfalseans", "group": "Ungrouped variables", "definition": "[if(len(set(A)-set(B))=0,if(len(set(B)-set(A))>0,1,0),0),\n  if(len(set(A)-set(B))=0,1,0),\n  if(len(set(A)-set(B))=0,0,1),\n  if(len(set(A)-set(B))=0,if(len(set(B)-set(A))=0,1,0),1),\n  if(len(set(B)-set(A[0])) = len(set(B)),0,1),\n  if(len(set(A)-set(B[1])) = len(set(A)),1,0)\n  ]", "description": "", "templateType": "anything", "can_override": false}, "t1": {"name": "t1", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{n[0]} \\\\subset \\\\var{n[1]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "t2": {"name": "t2", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{n[0]} \\\\subseteq \\\\var{n[1]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "t3": {"name": "t3", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{n[0]} \\\\not \\\\subseteq \\\\var{n[1]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "t4": {"name": "t4", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{n[0]} \\\\not \\\\subset \\\\var{n[1]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "t5": {"name": "t5", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{A[0]} \\\\in \\\\var{n[1]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}, "t6": {"name": "t6", "group": "Ungrouped variables", "definition": "\"<p>$\\\\var{B[1]} \\\\notin \\\\var{n[0]}$</p>\"", "description": "", "templateType": "long string", "can_override": false}}, "variablesTest": {"condition": "length(A)>1 AND length(B)>1 AND length(AnB)>0", "maxRuns": "7"}, "ungrouped_variables": ["length", "A", "B", "justA", "justB", "AnB", "AuB", "n", "AWrite", "Bwrite", "notAnB", "trueorfalse", "trueorfalseans", "t1", "t2", "t3", "t4", "t5", "t6"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "list-of-numbers", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the set $\\var{n[0]} \\cap \\var{n[1]}$</p>", "settings": {"correctAnswer": "AnB", "allowFractions": false, "correctAnswerFractions": false, "isSet": false, "show_input_hint": true, "separator": ","}}, {"type": "list-of-numbers", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the set $\\var{n[0]} \\cup \\var{n[1]}$</p>", "settings": {"correctAnswer": "AuB", "allowFractions": false, "correctAnswerFractions": false, "isSet": true, "show_input_hint": true, "separator": ","}}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Select all statements that are true</p>", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": "trueorfalse", "matrix": "trueorfalseans"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}