1) $S=\\{y\\;|\\;y \\in \\mathbb{Z}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$
\n$S\\;$=[[0]]
\n2) $S=\\{y\\;|\\;y \\in \\mathbb{N}, y=\\var{a}x-\\var{c},\\;x \\in \\mathbb{Z}\\text{ and } |y| \\leq \\var{b}\\}$
\n$S\\;$=[[1]]
\n3) $S=\\{x\\:| x \\in \\mathbb{Z}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.
\n$S=\\;$[[2]]
\n4) $S=\\{x\\:| x \\in \\mathbb{N}\\text{ and }\\;|\\var{a1}x-\\var{c1}| \\leq \\var{b1}\\}$.
\n$S=\\;$[[3]]
", "scripts": {}, "marks": 0, "type": "gapfill"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "{set(-c2+1..c2-1)}", "vsetrange": [0, 1], "checkingtype": "absdiff", "scripts": {}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "showpreview": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "checkvariablenames": false, "type": "jme", "vsetrangepoints": 5}, {"answer": "{set(g*ceil((-c3+1)/g)..(c3-1)#g)}", "vsetrange": [0, 1], "checkingtype": "absdiff", "scripts": {}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "showpreview": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "checkvariablenames": false, "type": "jme", "vsetrangepoints": 5}], "variableReplacements": [], "showCorrectAnswer": true, "prompt": "1) $S=\\{\\var{a2}a+\\var{b2}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a2}a+\\var{b2}b\\,|\\lt \\var{c2}\\}$.
\n$S=\\;$[[0]]
\n2) $S=\\{\\var{a3}a+\\var{b3}b\\;|\\;a,\\;b \\in \\mathbb{Z},\\;|\\var{a3}a+\\var{b3}b\\,|\\lt \\var{c3}\\}$.
\n$S=\\;$[[1]]
\n", "scripts": {}, "marks": 0, "type": "gapfill"}], "name": "Luis's copy of set4-", "ungrouped_variables": ["a", "b", "c", "ans1", "ans2", "a1", "b1", "c1", "ans3", "ans4", "a2", "b2", "c2", "a3", "b3", "c3", "g"], "variables": {"ans4": {"description": "", "definition": "ans3 and set(1..floor((c1+b1)/a1))", "templateType": "anything", "name": "ans4", "group": "Ungrouped variables"}, "g": {"description": "", "definition": "gcd(a3,b3)", "templateType": "anything", "name": "g", "group": "Ungrouped variables"}, "ans1": {"description": "", "definition": "set(a*ceil((c-b)/a)-c..a*floor((c+b)/a)-c#a)", "templateType": "anything", "name": "ans1", "group": "Ungrouped variables"}, "b2": {"description": "", "definition": "random(2..12)", "templateType": "anything", "name": "b2", "group": "Ungrouped variables"}, "b": {"description": "", "definition": "random(2..10)", "templateType": "anything", "name": "b", "group": "Ungrouped variables"}, "b1": {"description": "", "definition": "random(6..10 except b)", "templateType": "anything", "name": "b1", "group": "Ungrouped variables"}, "a": {"description": "", "definition": "random(2..6)", "templateType": "anything", "name": "a", "group": "Ungrouped variables"}, "c2": {"description": "", "definition": "random(4..10)", "templateType": "anything", "name": "c2", "group": "Ungrouped variables"}, "a1": {"description": "", "definition": "random(2..6 except a)", "templateType": "anything", "name": "a1", "group": "Ungrouped variables"}, "ans2": {"description": "", "definition": "ans1 and set(1..b)", "templateType": "anything", "name": "ans2", "group": "Ungrouped variables"}, "a3": {"description": "", "definition": "random(2..15)", "templateType": "anything", "name": "a3", "group": "Ungrouped variables"}, "c": {"description": "", "definition": "random(3..8)", "templateType": "anything", "name": "c", "group": "Ungrouped variables"}, "b3": {"description": "", "definition": "random(2..12)", "templateType": "anything", "name": "b3", "group": "Ungrouped variables"}, "a2": {"description": "", "definition": "random(2..6)", "templateType": "anything", "name": "a2", "group": "Ungrouped variables"}, "c1": {"description": "", "definition": "random(3..6 except c)", "templateType": "anything", "name": "c1", "group": "Ungrouped variables"}, "ans3": {"description": "", "definition": "set(ceil((c1-b1)/a1)..floor((c1+b1)/a1))", "templateType": "anything", "name": "ans3", "group": "Ungrouped variables"}, "c3": {"description": "", "definition": "random(6..10)", "templateType": "anything", "name": "c3", "group": "Ungrouped variables"}}, "preamble": {"css": "", "js": ""}, "statement": "Enumerate each of the following sets.
\n\nNote that you input sets in the form set(a,b,c,..,z) .
For example set(1,2,3)gives the set $\\{1,2,3\\}$.
The empty set is input as set().
Also some labour saving tips:
\nIf you want to input all integers between $a$ and $b$ inclusive then instead of writing all the elements you can input this as set(a..b).
If you want to input all integers between $a$ and $b$ inclusive in steps of $c$ then this is input as set(a..b#c). So all odd integers from $-3$ to $28$ are input as set(-3..28#2).