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{"name": "Blathnaid's copy of Predicates and sets", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>Questions about logical predicates,&nbsp;and basic set theory concepts.</p>", 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"marks": 1, "vsetrangepoints": 5}, {"answer": "{ans3}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{ans4}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>1) $S=\\{y\\;|\\;y \\in \\mathbb{Z}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[0]]</p>\n<p>2) $S=\\{y\\;|\\;y \\in \\mathbb{N}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$</p>\n<p>$S\\;$=[[1]]</p>\n<p>3)&nbsp;$S=\\{x\\:| x \\in \\mathbb{Z}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[2]]</p>\n<p>4) $S=\\{x\\:| x \\in \\mathbb{N}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.</p>\n<p>$S=\\;$[[3]]</p>", "variableReplacements": [], "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "gaps": [{"answer": "{set(-c2+1..c2-1)}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}, {"answer": "{set(g*ceil((-c3+1)/g)..(c3-1)#g)}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "prompt": "<p>1) $S=\\{\\var{a2}a+\\var{b2}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a2}a+\\var{b2}b\\,|\\lt \\var{c2}\\}$.</p>\n<p>$S=\\;$[[0]]</p>\n<p>2) $S=\\{\\var{a3}a+\\var{b3}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a3}a+\\var{b3}b\\,|\\lt \\var{c3}\\}$.</p>\n<p>$S=\\;$[[1]]</p>\n<p></p>", "variableReplacements": [], "marks": 0}], "statement": "<p>Enumerate each of the following sets.</p>\n<p></p>\n<p>Note that you input sets in the form <code>set(a,b,c,..,z)</code> .</p>\n<p>For example <code> set(1,2,3)</code>gives the set $\\{1,2,3\\}$.</p>\n<p>The empty set is input as&nbsp;<code>set()</code>.</p>\n<p>Also some labour saving tips:</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as <code>set(a..b)</code>.</p>\n<p>If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as <code>set(a..b#c)</code>. So all odd integers from $-3$ to $28$ are input as&nbsp;<code>set(-3..28#2).</code></p>", "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "gcd(a2,b2)=1 and gcd(a3,b3)<>1", "maxRuns": "200"}, "advice": ""}]}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}], "extensions": [], "custom_part_types": [], "resources": []}