// Numbas version: finer_feedback_settings
{"name": "Lois's copy of set5 - Cartesian Products", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<h4>a)</h4>\n<p>$A \\times B$ is the set of all pairs $(a,b)$, where $a \\in A$ and $b \\in B$.</p>\n<h4>b)</h4>\n<p>$B \\cap D$ is the set of all elements present in both $B$ and $D$, i.e. $\\var{set2 and set5}$.</p>\n<p>$A \\cap C$ is the set of all elements present in both $A$ and $C$, i.e. $\\var{set1 and set4}$.</p>\n<p>$(B\\cap D)\\times (A\\cap C)$ is the set of pairs of&nbsp;all pairs $(x,y)$, where $x \\in B \\cap D$ and $y \\in A \\cap C$.</p>\n<h4>c)</h4>\n<p>$(A\\cap C)\\times (A\\cap C)\\times (C\\cap D)$ is the set of all triples $(x,y,z)$, where $x \\in A \\cap C$, $y \\in A \\cap C$ and $z \\in C \\cap D$. Note that $x$ and $y$&nbsp;do not have to be different.</p>\n<h4>d)</h4>\n<p>$A-C$ is the set of all elements present in $A$ but not in $C$, i.e. $\\var{set1-set4}$.</p>\n<p>$C-A$ is the set of all elements present in $C$ but not in $A$, i.e. $\\var{set4-set1}$.</p>\n<p>$(A-C) \\cup (C-A)$ is the set of all elements which are either in $A-C$, or in &nbsp;$C-A$, so $(A-C) \\cup (C-A) = \\var{(set1-set4) or (set4-set1)}$.</p>\n<h4>e)</h4>\n<p>$(A \\times D)$ is the set of all pairs of elements $(a,d)$, with $a \\in A$ and $d \\in D$,&nbsp;i.e. $\\var{set(product(list(set1),list(set5)))}$.</p>\n<p>$C \\times B)$ is the set of all pairs of elements $(c,b)$, with $c \\in C$ and $b \\in B$, i.e. $\\var{set(product(list(set4),list(set2)))}$.</p>\n<p>$(A \\times D) \\cap (C \\times B)$ is the set of all pairs present in both of the previous sets.</p>\n<h4>f)</h4>\n<p>$C \\cap D$ is the set of all elements in both $C$ and in $D$, so $C \\cap D = \\var{(set4 and set5)}$.</p>\n<p>$C - D$ is the set of all elements in $C$ and not in $D$, so $C-D = \\var {(set4 - set5)}$.</p>\n<p>$(C \\cap D) \\times (C - D)$ is the set of all pairs of elements $(x,y)$, where $x$ is in $C \\cap D$ and $y$ is in $C - D$, so $(C \\cap D) \\times (C-D) = \\var{set(product(list(set4 and set5),list(set4 - set5)))}$.</p>\n<p>Similarly, $(D - C) \\times (C \\cap D) = \\var{set(product(list(set5-set4),list(set4 and set5)))}$.</p>\n<p>Finally, $[(C \\cap D) \\times (C - D)] \\cup [(D - C) \\times (C \\cap D)]$ is the set of all pairs present in either of the above sets, i.e. $\\var{set16}$.</p>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Lois's copy of set5 - Cartesian Products", "statement": "<p>Let $A=\\var{set1}$,&nbsp; let&nbsp; $B=\\var{set2}$, let&nbsp; $C=\\var{set4}$ and let $D=\\var{set5}$.</p>\n<p>List the elements of the following sets.</p>\n<p>Input sets in the form <code>set(a,b,c,d)</code> .</p>\n<p>For example <code> set(1,2,3)&nbsp;</code>gives the set $\\{1,2,3\\}$.</p>\n<p>Element $(a,b)$ of a Cartesian product is entered, and represented, as $[a,b]$.</p>\n<p>For example <code> set([1,1],[1,2],[2,3])</code>gives the set $\\{[1,1], [1,2], [2,3]\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>", "functions": {"mod_set": {"type": "list", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "language": "javascript", "definition": "//returns all integers which are divisible by c betweeen a and b\nvar l=[];\nfor(var i=a;i<b+1;i++) \n{ if (i%c==0){l.push(i);}\n}\nreturn l;\n"}}, "variable_groups": [{"variables": ["a", "b"], "name": "Random numbers"}, {"variables": ["list1", "list2", "list4", "list5", "list9", "list10", "list_extra"], "name": "Lists"}], "ungrouped_variables": ["set1", "set2", "set3", "set4", "set5", "set6", "set7", "set8", "set10", "set11", "set12", "set14", "set15", "set16"], "preamble": {"js": "", "css": ""}, "parts": [{"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set3}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$A \\times B=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set6}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$(B\\cap D)\\times (A\\cap C)=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set10}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$(A\\cap C)\\times (A\\cap C)\\times (C\\cap D)=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set14}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$[(A - C)\\cup (C-A)]\\times [(B-D)\\cup(D-B)]=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set15}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$(A\\times D)\\cap (C\\times B)=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}, {"gaps": [{"type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "answer": "{set16}", "showFeedbackIcon": true, "checkingtype": "absdiff", "checkvariablenames": false, "checkingaccuracy": 0.001, "showpreview": true, "scripts": {}, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>$[(C\\cap D)\\times (C-D)]\\cup [(D-C)\\times (C\\cap D)]=\\;$[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "showFeedbackIcon": true}], "variables": {"set12": {"group": "Ungrouped variables", "definition": "union(set2-set5,set5-set2)", "name": "set12", "templateType": "anything", "description": ""}, "list10": {"group": "Lists", "definition": "map(list9[x][0]+list9[x][1],x,0..len(list9)-1)", "name": "list10", "templateType": "anything", "description": ""}, "set8": {"group": "Ungrouped variables", "definition": "intersection(set2,set5)", "name": "set8", "templateType": "anything", "description": ""}, "list5": {"group": "Lists", "definition": "shuffle(list2)[0..b-1]+list_extra", "name": "list5", "templateType": "anything", "description": ""}, "a": {"group": "Random numbers", "definition": "random(2..3)", "name": "a", "templateType": "anything", "description": ""}, "set5": {"group": "Ungrouped variables", "definition": "set(list5)", "name": "set5", "templateType": "anything", "description": ""}, "set14": {"group": "Ungrouped variables", "definition": "set(product(list(set11),list(set12)))", "name": "set14", "templateType": "anything", "description": ""}, "set16": {"group": "Ungrouped variables", "definition": "union(set(product(list(intersection(set4,set5)),list(set4-set5))),set(product(list(set5-set4),list(intersection(set4,set5)))))", "name": "set16", "templateType": "anything", "description": ""}, "set10": {"group": "Ungrouped variables", "definition": "set(list10)", "name": "set10", "templateType": "anything", "description": ""}, "set15": {"group": "Ungrouped variables", "definition": "intersection(set(product(list1,list5)),set(product(list4,list2)))", "name": "set15", "templateType": "anything", "description": ""}, "set4": {"group": "Ungrouped variables", "definition": "set(list4)", "name": "set4", "templateType": "anything", "description": ""}, "list9": {"group": "Lists", "definition": "product(product(list(set7),list(set7)),list(intersection(set4,set5)))", "name": "list9", "templateType": "anything", "description": ""}, "list2": {"group": "Lists", "definition": "shuffle(list(25..100#5))[0..b]", "name": "list2", "templateType": "anything", "description": ""}, "b": {"group": "Random numbers", "definition": "5-a", "name": "b", "templateType": "anything", "description": ""}, "list1": {"group": "Lists", "definition": "shuffle(list(1..20))[0..a]", "name": "list1", "templateType": "anything", "description": ""}, "set3": {"group": "Ungrouped variables", "definition": "set(product(list1,list2))", "name": "set3", "templateType": "anything", "description": ""}, "set2": {"group": "Ungrouped variables", "definition": "set(list2)", "name": "set2", "templateType": "anything", "description": ""}, "list4": {"group": "Lists", "definition": "shuffle(list1)[0..a-1]+list_extra", "name": "list4", "templateType": "anything", "description": ""}, "set7": {"group": "Ungrouped variables", "definition": "intersection(set1,set4)", "name": "set7", "templateType": "anything", "description": ""}, "set6": {"group": "Ungrouped variables", "definition": "set(product(list(set8),list(set7)))", "name": "set6", "templateType": "anything", "description": ""}, "set1": {"group": "Ungrouped variables", "definition": "set(list1)", "name": "set1", "templateType": "anything", "description": ""}, "set11": {"group": "Ungrouped variables", "definition": "union(set1-set4,set4-set1)", "name": "set11", "templateType": "anything", "description": ""}, "list_extra": {"group": "Lists", "definition": "[random(21..24)]", "name": "list_extra", "templateType": "anything", "description": ""}}, "extensions": [], "rulesets": {}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}