"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, 0, 8, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},
- or 5 consecutive elements centred around 0 e.g.{...-4,-2,0,2,4...} or 6 consecutive elements centred around 0 e.g.{...-9,-3,-1,1,3,9...}.

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; if(abintersection_string == ""){Correct%QUESTION.NUMBER% = "{"+universal+"}"} else (Correct%QUESTION.NUMBER% = "{"+complement+"}") //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback1%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}.

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = {"+abintersection_string+"}.

The complement of the intersection of two sets A and B, denoted (A∩B)^{c}, is the set of elements which belong to U but which do not belong to A∩B.

Therefore, the correct answer for (A∩B)^{c} should be "+Correct%QUESTION.NUMBER%+" ";
Feedback2%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}.

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = ∅ (empty set).

The complement of the intersection of two sets A and B, denoted (A∩B)^{c}, is the set of elements which belong to U but which do not belong to A∩B. Since the set A∩B does not contain any elements, its complement is the universal set.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; feedback = ""; if(Correct%QUESTION.NUMBER% == "{"+universal+"}"){feedback = Feedback2%QUESTION.NUMBER%;} else {feedback = Feedback1%QUESTION.NUMBER%;} Feedback%QUESTION.NUMBER% = feedback; document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 6, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},
- or 5 consecutive elements centred around 0 e.g.{...-4,-2,0,2,4...} or 6 consecutive elements centred around 0 e.g.{...-9,-3,-1,1,3,9...}.

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; Correct%QUESTION.NUMBER% = "{}" //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}.

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = {"+abintersection+"}.

The complement of the intersection of two sets A and B, denoted (A∩B)^{c}, is the set of elements which belong to U but which do not belong to A∩B. Since the set A∩B = {"+abintersection+"} = U (universal set) there is no such elements of the universal set that are not in A∩B.

Therefore, (A∩B)^{c} (the complement of the intersection of two sets A and B) is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},
- or 5 consecutive elements centred around 0 e.g.{...-4,-2,0,2,4...} or 6 consecutive elements centred around 0 e.g.{...-9,-3,-1,1,3,9...}.

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; Correct%QUESTION.NUMBER% = "{"+universal+"}" //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = ∅ (empty set).

The complement of the intersection of two sets A and B, denoted (A∩B)^{c}, is the set of elements which belong to U but which do not belong to A∩B. Since the set A∩B does not contain any elements, its complement is the universal set.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, 0, 8, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(abintersection_string,universal_string); if(complement == ""){Correct%QUESTION.NUMBER% = "{}"} else if(abintersection_string == ""){Correct%QUESTION.NUMBER% = "{"+universal+"}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback1%QUESTION.NUMBER%="

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = {"+abintersection_string+"}.

The complement of the intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to U but which do not belong to A∩B.

Therefore, the correct answer for (A∩B)^{c} should be "+Correct%QUESTION.NUMBER%+" ";
Feedback2%QUESTION.NUMBER%="

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = {"+abintersection_string+"}.

The complement of the intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to U but which do not belong to A∩B. Since the set A∩B = {"+abintersection_string+"} = U (universal set) there is no such elements of the universal set that are not in A∩B.

Therefore, (A∩B)^{c} (the complement of the intersection of two sets A and B) is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
Feedback3%QUESTION.NUMBER%="

The intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to both A and B. Since A = {"+aset+"} and B = {"+bset+"}, A∩B = ∅ (empty set).

The complement of the intersection of two sets A and B, denoted by A∩B, is the set of elements which belong to U but which do not belong to A∩B. Since the set A∩B does not contain any elements, its complement is the universal set.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; feedback = ""; if(Correct%QUESTION.NUMBER% == "{}"){feedback = Feedback2%QUESTION.NUMBER%;} else if(Correct%QUESTION.NUMBER% == "{"+universal+"}"){feedback = Feedback3%QUESTION.NUMBER%;} else {feedback = Feedback1%QUESTION.NUMBER%;} Feedback%QUESTION.NUMBER% = feedback; document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; Correct%QUESTION.NUMBER% = "{"+complement+"}" //document.write(Correct%QUESTION.NUMBER%+"

"+cset); Feedback%QUESTION.NUMBER%="

The union of two sets A and B, denoted by A∪B, is the set of all elements which belong to A or to B. Since A = {"+aset+"} and B = {"+bset+"}, A∪B = {"+abunion_string+"}.

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B.

Therefore, the correct answer for (A∪B)^{c} should be "+Correct%QUESTION.NUMBER%+" ";
document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(abunion_string,universal_string); if(complement == ""){Correct%QUESTION.NUMBER% = "{}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The union of two sets A and B, denoted by A∪B, is the set of all elements which belong to A or to B. Since A = {"+aset+"} and B = {"+bset+"}, A∪B = {"+abunion_string+"}.

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B. Since the set A∪B = {"+abunion_string+"} = U (universal set) there is no such elements of the universal set that are not in A∪B.

Therefore, (A∪B)^{c} (the complement of the union of two sets A and B) is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

input ^{c} explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(abunion_string,universal_string); if(complement == ""){Correct%QUESTION.NUMBER% = "{}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"+cset); Feedback1%QUESTION.NUMBER%="

The union of two sets A and B, denoted by A∪B, is the set of all elements which belong to A or to B. Since A = {"+aset+"} and B = {"+bset+"}, A∪B = {"+abunion_string+"}.

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B.

Therefore, the correct answer for (A∪B)^{c} should be "+Correct%QUESTION.NUMBER%+" ";
Feedback2%QUESTION.NUMBER%="

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B. Since the set A∪B = {"+abunion_string+"} = U (universal set) there is no such elements of the universal set that are not in A∪B.

Therefore, (A∪B)^{c} (the complement of the union of two sets A and B) is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
feedback = "";
if(Correct%QUESTION.NUMBER% == "{}"){feedback = Feedback2%QUESTION.NUMBER%;}
else {feedback = Feedback1%QUESTION.NUMBER%;}
Feedback%QUESTION.NUMBER% = feedback;
document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

^{c} = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; e2=""; Equation2%QUESTION.NUMBER% = m1+m2+m3+e2; Equation%QUESTION.NUMBER% = Equation1%QUESTION.NUMBER%+Equation2%QUESTION.NUMBER%; QuestionText0%QUESTION.NUMBER% = "Let the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and two sets

"
QuestionText2%QUESTION.NUMBER% = "

Set C comprises elements that are neither in A nor in B. Input C explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(abunion_string,universal_string); if(complement == ""){Correct%QUESTION.NUMBER% = "{}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"+cset); Feedback1%QUESTION.NUMBER%="

Set C comprises elements that are neither in A nor in B i.e. its elements are not in A and not in B. Therefore, they are in the complement of A and in the complement of B. This is equivalent to the complement of the union of A and B, denoted (A∪B)^{c}.

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B.

Therefore, the correct answer for (A∪B)^{c} should be "+Correct%QUESTION.NUMBER%+" ";
Feedback2%QUESTION.NUMBER%="

Set C comprises elements that are neither in A nor in B i.e. its elements are not in A and not in B. Therefore, they are in the complement of A and in the complement of B. This is equivalent to the complement of the union of A and B, denoted (A∪B)^{c}.

The complement of the union of two sets A and B, denoted (A∪B)^{c}, is the set of elements which belong to U but which do not belong to A∪B. Since the set A∪B = {"+abunion_string+"} = U (universal set) there is no such elements of the universal set that are not in A∪B.

Therefore, (A∪B)^{c} (the complement of the union of two sets A and B) is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
feedback = "";
if(Correct%QUESTION.NUMBER% == "{}"){feedback = Feedback2%QUESTION.NUMBER%;}
else {feedback = Feedback1%QUESTION.NUMBER%;}
Feedback%QUESTION.NUMBER% = feedback;
document.write(QuestionText0%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; QuestionText1%QUESTION.NUMBER% = "

and set

"
QuestionText2%QUESTION.NUMBER% = "

input *A* explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(aset_string,universal_string); Correct%QUESTION.NUMBER% = "{"+complement+"}" //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = {"+aset+"}, its complement is the set of all elements in the universal set that are not in A.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; document.write(QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

*A* = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set n = displayarray( 1, 1, 5, 1); myAArray = displayarray( n, -4, 11, 1); a_set = ""; for(ip=0; ip

"; QuestionText1%QUESTION.NUMBER% = "

and set

"
QuestionText2%QUESTION.NUMBER% = "

input *A* explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; Correct%QUESTION.NUMBER% = "{}" //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = "+aset+" = U there is no such elements of the universal set that are not in A .

Therefore, the complement of the set A is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+""; document.write(QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

*A* = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { ///////////////// A set aset = "∅" ///////////////// B set m = displayarray( 1, 1, 5, 1); myBArray = displayarray( m, -4, 11, 1); b_set = ""; for(ip=0; ip

"; QuestionText1%QUESTION.NUMBER% = "

and set

"
QuestionText2%QUESTION.NUMBER% = "

input *A* explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; Correct%QUESTION.NUMBER% = "{"+universal+"}" //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback%QUESTION.NUMBER%="

The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = ∅ (A is the empty set), its complement is the universal set.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; document.write(QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

*A* = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { myAArray = displayarray( 5, -4, 12, 1); myBArray = displayarray( 5, -4, 12, 1); var a_set = new Array(""+myAArray[0]+"", ""+myAArray[1]+"", ""+myAArray[2]+"", ""+myAArray[3]+"", ""+myAArray[4]+""); aset = a_set.sort(function(a,b){return a - b}); aset_string=aset.join(); var b_set = new Array(""+myBArray[0]+"", ""+myBArray[1]+"", ""+myBArray[2]+"", ""+myBArray[3]+"", ""+myBArray[4]+""); bset = b_set.sort(function(a,b){return a - b}); bset_string=bset.join(); universal = set_union(aset_string,bset_string); universal_string=universal.join(); if(myAArray[0] == 1 || myAArray[0] == 2){aset= "{"+universal+"}"} else if(myAArray[0] == 3 || myAArray[0] == 4){aset = "∅"} else {aset = "{"+aset+"}"} nwidth=getFontSize()/16*250 nheight=getFontSize()/16*60 m1="" Equation1%QUESTION.NUMBER% = m1+m2+m3+e1; e0=""; Equation0%QUESTION.NUMBER% = m1+m2+m3+e0; QuestionText0%QUESTION.NUMBER% = "Given the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and set

"
QuestionText2%QUESTION.NUMBER% = "

input *A* explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(aset_string,universal_string); if(myAArray[0] == 1 || myAArray[0] == 2 || universal_string == aset_string){Correct%QUESTION.NUMBER% = "{}"} else if(myAArray[0] == 3 || myAArray[0] == 4){Correct%QUESTION.NUMBER% = "{"+universal+"}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback1%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = "+aset+", its complement is the set of all elements in the universal set that are not in A. Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" ";
Feedback2%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = "+aset+" = U there is no such elements of the universal set that are not in A . Therefore, the complement of the set A is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+"";
Feedback3%QUESTION.NUMBER%="

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. The complement set, denoted *A*, is the set of elements which belong to U but which do not belong to A. Since the set A = ∅ (A is the empty set), its complement is the universal set. Therefore, the correct answer should be the universal set "+Correct%QUESTION.NUMBER%+" ";
feedback = "";
if(Correct%QUESTION.NUMBER% == "{}"){feedback = Feedback2%QUESTION.NUMBER%;}
else if(Correct%QUESTION.NUMBER% == "{"+universal+"}"){feedback = Feedback3%QUESTION.NUMBER%;}
else {feedback = Feedback1%QUESTION.NUMBER%;}
Feedback%QUESTION.NUMBER% = feedback;
document.write(QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%);
document.write("

*A* = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>

"} else {document.forms[0].elements[item+3].value = "Your answer,

"+ANS+"

"+SHOW+" "} document.forms[0].elements[item+3].value = QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+ QuestionText3%QUESTION.NUMBER%+document.forms[0].elements[item+3].value } function question%QUESTION.NUMBER%() { myAArray = displayarray( 5, -4, 12, 1); myBArray = displayarray( 5, -4, 12, 1); var a_set = new Array(""+myAArray[0]+"", ""+myAArray[1]+"", ""+myAArray[2]+"", ""+myAArray[3]+"", ""+myAArray[4]+""); aset = a_set.sort(function(a,b){return a - b}); aset_string=aset.join(); var b_set = new Array(""+myBArray[0]+"", ""+myBArray[1]+"", ""+myBArray[2]+"", ""+myBArray[3]+"", ""+myBArray[4]+""); bset = b_set.sort(function(a,b){return a - b}); bset_string=bset.join(); universal = set_union(aset_string,bset_string); universal_string=universal.join(); if(myAArray[0] == 1 || myAArray[0] == 2){aset= "{"+universal+"}"} else if(myAArray[0] == 3 || myAArray[0] == 4){aset = "∅"} else {aset = "{"+aset+"}"} nwidth=getFontSize()/16*250 nheight=getFontSize()/16*60 m1="" Equation1%QUESTION.NUMBER% = m1+m2+m3+e1; e0=""; Equation0%QUESTION.NUMBER% = m1+m2+m3+e0; QuestionText0%QUESTION.NUMBER% = "Let the universal set

"; QuestionText1%QUESTION.NUMBER% = "

and set

"
QuestionText2%QUESTION.NUMBER% = "

Set C comprises elements that are not in A. Input C explicitly with elements in numerical order:

"; QuestionText3%QUESTION.NUMBER% = "

__Important:__ input your answer without spaces, separating each element with a comma and in ascending order e.g. {11,12,13}

If you think the set has an infinite number of elements, input

- 5 consecutive elements at the start e.g. {7,8,9,10,11...},
- or 5 consecutive elements at the end e.g. {...-1,0,1,2,3},

If you think the set is empty, input

"; QuestionText%QUESTION.NUMBER% = QuestionText0%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%+QuestionText3%QUESTION.NUMBER%; complement = set_complement(aset_string,universal_string); if(myAArray[0] == 1 || myAArray[0] == 2 || universal_string == aset_string){Correct%QUESTION.NUMBER% = "{}"} else if(myAArray[0] == 3 || myAArray[0] == 4){Correct%QUESTION.NUMBER% = "{"+universal+"}"} else {Correct%QUESTION.NUMBER% = "{"+complement+"}"} //document.write(Correct%QUESTION.NUMBER%+"

"); Feedback1%QUESTION.NUMBER%="

Set C comprises elements that are not in A i.e. its elements are in the complement of A. This is denoted by *A* and is the set of elements which do not belong to A but which belong to the universal set.

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. Since the set A = "+aset+", its complement is the set of all elements in the universal set that are not in A. Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; Feedback2%QUESTION.NUMBER%="

Set C comprises elements that are not in A i.e. its elements are in the complement of A. This is denoted by *A* and is the set of elements which do not belong to A but which belong to the universal set.

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. Since the set A = "+aset+" = U there is no such elements of the universal set that are not in A . Therefore, the complement of the set A is empty and so the correct answer should be "+Correct%QUESTION.NUMBER%+""; Feedback3%QUESTION.NUMBER%="

Set C comprises elements that are not in A i.e. its elements are in the complement of A. This is denoted by *A* and is the set of elements which do not belong to A but which belong to the universal set.

The universal set is a set containing all elements of a problem under consideration. In the question, the universal set is given by U = {"+universal+"}. Since the set A = ∅ (A is the empty set), its complement is the universal set.

Therefore, the correct answer should be "+Correct%QUESTION.NUMBER%+" "; feedback = ""; if(Correct%QUESTION.NUMBER% == "{}"){feedback = Feedback2%QUESTION.NUMBER%;} else if(Correct%QUESTION.NUMBER% == "{"+universal+"}"){feedback = Feedback3%QUESTION.NUMBER%;} else {feedback = Feedback1%QUESTION.NUMBER%;} Feedback%QUESTION.NUMBER% = feedback; document.write(QuestionText0%QUESTION.NUMBER%+Equation1%QUESTION.NUMBER%+QuestionText1%QUESTION.NUMBER%+Equation0%QUESTION.NUMBER%+QuestionText2%QUESTION.NUMBER%); document.write("

*C* = ")
document.write(QuestionText3%QUESTION.NUMBER%);
document.write("")
}
if (document.forms[0].name=="FEEDBACK")
{}
else
{question%QUESTION.NUMBER%()}
]]>

"+""+"

") } ]]>