Consider the set $S=\\{\\var{a},\\emptyset,\\var{b},\\var{c}\\}$. Which of the following statements are true? More than one of these may be a true statement. Note that you will lose marks if you tick a box as true when it is in fact false.
", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\var{a}\\in S$", "$\\{\\var{a}\\}\\in S$", "$\\var{b}\\subseteq S$", "$\\{\\var{b}\\}\\subseteq S$", "$\\emptyset\\in S$", "$\\{\\emptyset\\}\\in S$"], "matrix": ["1", "-1", "-1", "1", "1", "-1"], "distractors": ["", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Cardinality", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Zworestine", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12364/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(100..999)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(100..999)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "(a)", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the cardinality of the set $\\{\\var{a},j,a,m,e,s,e,a,s,t,\\var{a}\\}$?
", "minValue": "7", "maxValue": "7", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "(b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the cardinality of the set $\\{0,\\emptyset\\}$?
", "minValue": "2", "maxValue": "2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "(c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the cardinality of the set $\\{4,5,6,7,\\ldots,\\var{b}\\}$?
", "minValue": "{b}-3", "maxValue": "{b}-3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Match set to its power set", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Zworestine", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12364/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..10 except a)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Match each set on the left to its power set.
", "minMarks": "0", "maxMarks": "4", "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\{\\var{a}\\}$", "$\\{\\var{a},\\var{b}\\}$", "$\\emptyset$", "$\\{0,\\emptyset\\}$"], "matrix": [[0, "1", 0, 0], [0, 0, "1", 0], ["1", 0, 0, 0], [0, 0, 0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["$\\{\\emptyset\\}$", "$\\{\\emptyset,\\{\\var{a}\\}\\}$", "$\\{\\emptyset,\\{\\var{a}\\},\\{\\var{b}\\},\\{\\var{a},\\var{b}\\}\\}$", "$\\{\\emptyset,\\{0\\},\\{\\emptyset\\},\\{0,\\emptyset\\}\\}$"], "choicesHeader": "", "answersHeader": ""}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": false, "showfrontpage": true, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "Oscar2", "autoSubmit": true, "allowAttemptDownload": false, "downloadEncryptionKey": "", "showresultspage": "oncompletion"}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "inreview", "showtotalmarkwhen": "inreview", "showanswerstatewhen": "inreview", "showpartfeedbackmessageswhen": "inreview", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": false, "intro": "", "end_message": "", "results_options": {"printquestions": true, "printadvice": false}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": false, "reviewshowfeedback": true, "showactualmark": false, "showtotalmark": false, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Charles Zworestine", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12364/"}], "extensions": [], "custom_part_types": [], "resources": []}