How many sets is in the partition of "+letter+"?
" QuestionText%QUESTION.NUMBER% = QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%; remainders = ""; for(ib = 0; ib < d; ib++){ remainders += ib+","} remainders=remainders.slice(0, remainders.length-1); aset%QUESTION.NUMBER% = ""; for(ib = b; ib < c; ib++){ aset%QUESTION.NUMBER% += ib+","} aset%QUESTION.NUMBER% += (c)+""; Correct%QUESTION.NUMBER% = d; //document.write("+Correct%QUESTION.NUMBER%+"
"); Feedback%QUESTION.NUMBER%="
A partition of a set "+letter+" is a collection of nonempty subsets such that those subsets are mutually disjoint (no two sets have any elements in common) and "+letter+" is the union of those sets.
The partition formed by the relation "+EquationText%QUESTION.NUMBER%+" is a collection of subsets, each containing elements x∈"+letter+" which divided by "+d+" give remainders y. Dividing any number by "+d+" results in one of the possible "+d+" remainders, i.e. "+remainders+".
According to the relation R these remainders are equivalent to any number formed by adding a (positive or negative) multiple of "+d+". These must be elements of "+letter +" and this forms the subsets of "+letter+".
Therefore, there are "+d+" subsets of the partition of "+letter+" and it should be your answer."; //document.write(Feedback%QUESTION.NUMBER%+"
"+QuestionText1%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write(QuestionText0%QUESTION.NUMBER%+EquationText%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+EquationText0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("") document.write("") } if (document.forms[0].name=="FEEDBACK") {} else {question%QUESTION.NUMBER%()} ]]>
";
QuestionText2%QUESTION.NUMBER% = "
Please answer YES or NO.
";
QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%;
allowed_input1 = "YES";
allowed_input2 = "NO";
if(intersectionab_string != "" || intersectionac_string != "" || intersectionbc_string != "" || m == 2){Correct%QUESTION.NUMBER% = "NO"}
else (Correct%QUESTION.NUMBER% = "YES")
//document.write(Correct%QUESTION.NUMBER%+"
"); Feedback1%QUESTION.NUMBER%="
A partition of a set A is a collection of nonempty subsets A1, A2, A3, ... such that those subsets are mutually disjoint (no two sets have any elements in common) and A is the union of those sets.
In the question, both conditions are broken. "+text+" in more than one set (excluding set A) and also -8 is present in set A but not in any other set, i.e. A1∪A2∪A3 ≠ A.
Therefore, {A1,A2,A3} is not a partition of A and your answer should be "+Correct%QUESTION.NUMBER%+". "; Feedback2%QUESTION.NUMBER%="
A partition of a set A is a collection of nonempty subsets A1, A2, A3, ... such that those subsets are mutually disjoint (no two sets have any elements in common) and A is the union of those sets.
In the question, the first condition is broken. "+text+" in more than one set (excluding set A).
Therefore, {A1,A2,A3} is not a partition of A and your answer should be "+Correct%QUESTION.NUMBER%+". "; Feedback3%QUESTION.NUMBER%="
A partition of a set A is a collection of nonempty subsets A1, A2, A3, ... such that those subsets are mutually disjoint (no two sets have any elements in common) and A is the union of those sets.
In the question, the second condition is broken. -8 is present in set A but not in any other set, i.e. A1∪A2∪A3 ≠ A.
Therefore, {A1,A2,A3} is not a partition of A and your answer should be "+Correct%QUESTION.NUMBER%+". "; Feedback4%QUESTION.NUMBER%="
A partition of a set A is a collection of nonempty subsets A1, A2, A3, ... such that those subsets are mutually disjoint (no two sets have any elements in common) and A is the union of those sets.
In the question, both conditions hold. Therefore, {A1,A2,A3} is a partition of A and your answer should be "+Correct%QUESTION.NUMBER%+". "; feed1=""; feed2=""; if(intersectionab_string != "" || intersectionac_string != "" || intersectionbc_string != ""){feed1="feed1"} if(m == 2){feed2="feed2"} feedback = ""; if(feed1=="feed1" && feed2=="feed2"){feedback = Feedback1%QUESTION.NUMBER%;} else if(feed1=="feed1"){feedback = Feedback2%QUESTION.NUMBER%;} else if(feed2=="feed2"){feedback = Feedback3%QUESTION.NUMBER%;} else {feedback = Feedback4%QUESTION.NUMBER%;} Feedback%QUESTION.NUMBER% = feedback; document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%); document.write("
") document.write(QuestionText2%QUESTION.NUMBER%); document.write("") } if (document.forms[0].name=="FEEDBACK") {} else {question%QUESTION.NUMBER%()} ]]>
What is the set A3 so that {A1,A2,A3} is a partition of A?
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QuestionText2%QUESTION.NUMBER% = "
Important: input your answer without spaces, separating each element with a comma and in ascending order e.g. {1,2,3}."
QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%;
Correct%QUESTION.NUMBER% = difference_display;
//document.write(Correct%QUESTION.NUMBER%+"
"); Feedback%QUESTION.NUMBER%="
A partition of a set A is a collection of nonempty subsets A1, A2, A3, ... such that those subsets are mutually disjoint (no two sets have any elements in common) and A is the union of those sets.
With A, A1 and A2 given, a way to find A3 is to firstly find A1∪A2
A1∪A2 = "+bset_display+" ∪ "+cset_display+" = "+unionbcset_display+".
Then you have to identify elements in A that are not in A1∪A2, i.e.
A \ (A1∪A2) = "+difference_display+".
This is your answer for A3 since this set does not contain any elements that are either in A1 or in A2, and A1∪A2∪A3 = A."; document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%); document.write("
A3 = ") document.write(QuestionText2%QUESTION.NUMBER%); document.write("") } if (document.forms[0].name=="FEEDBACK") {} else {question%QUESTION.NUMBER%()} ]]>
"+e+" is one of the elements of a subset in the partition of "+letter+".
State this subset.
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QuestionText3%QUESTION.NUMBER% = "
Important: input your answer without spaces, separating each element with a comma and in ascending order e.g. {1,2,3}."
QuestionText%QUESTION.NUMBER% = QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%;
remainders = "";
for(ib = 0; ib < d; ib++){
remainders += ib+","}
remainders=remainders.slice(0, remainders.length-1);
Correct = "";
for(ib = start; ib < c; ib=ib+d){
Correct += ib+","}
setlength=Correct.length;
Correct%QUESTION.NUMBER%="{"+Correct.slice(0, setlength-1)+"}";
//document.write(""+Correct%QUESTION.NUMBER%+"
"); Feedback1%QUESTION.NUMBER%="
A partition of a set "+letter+" is a collection of nonempty subsets such that those subsets are mutually disjoint (no two sets have any elements in common) and "+letter+" is the union of those sets.
The partition formed by the relation "+Equation1%QUESTION.NUMBER%+" is a collection of subsets, each containing elements x∈"+letter+" which divided by "+d+" give remainders y. Dividing any number by "+d+" results in one of the possible "+d+" remainders, i.e. "+remainders+".
According to the relation R these remainders are equivalent to any number formed by adding a (positive or negative) multiple of "+d+". These must be elements of "+letter +" and this forms the subsets of "+letter+".
Dividing "+e+" by "+d+" gives the remainder "+start1+". Since "+start1+" is not the element of set "+letter +" it is not the element of any subset of the partition. However, all the elements from "+letter+" giving "+start1+" as a remainder when divided by "+d+" form set "+Correct%QUESTION.NUMBER%+", that is a subset of the partition of "+letter +" and contains the required element "+e+"."; Feedback2%QUESTION.NUMBER%="
A partition of a set "+letter+" is a collection of nonempty subsets such that those subsets are mutually disjoint (no two sets have any elements in common) and "+letter+" is the union of those sets.
The partition formed by the relation "+Equation1%QUESTION.NUMBER%+" is a collection of subsets, each containing elements x∈"+letter+" which divided by "+d+" give remainders y. Dividing any number by "+d+" results in one of the possible "+d+" remainders, i.e. "+remainders+".
According to the relation R these remainders are equivalent to any number formed by adding a (positive or negative) multiple of "+d+". These must be elements of "+letter +" and this forms the subsets of "+letter+".
Dividing "+e+" by "+d+" gives the remainder "+start1+". Together with other elements from "+letter+", giving "+start1+" as a remainder when divided by "+d+", it forms set "+Correct%QUESTION.NUMBER%+", that is a subset of the partition of "+letter +" and contains the required element "+e+"."; if(start1") document.write(QuestionText3%QUESTION.NUMBER%); document.write("") } if (document.forms[0].name=="FEEDBACK") {} else {question%QUESTION.NUMBER%()} ]]>