#$&*
course Mth 151
7/27 11
Question: `q001. There are nine questions in this assignment.A group is a set and an operation on that set which has the properties of closure, associativity, identity and inverse. The set {1, 2} on the operation @ of Assignment 21, defined by x @ y = remainder when the product x * y is divided by 3, does have the associative property. Is the set {1, 2} a group on @?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Yes the set is a group
2
Ok
*********************************************
Question: `q002. Which of the properties closure, identity, commutativity, inverse, does the standard addition operation + have on the set {-1, 0, 1}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Commutative
2
Ok
*********************************************
Question: `q003. Does the operation * of standard multiplication on the set {-1, 0, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
Ok
*********************************************
Question: `q004. Does the operation * of standard multiplication on the set {-1, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
ok
*********************************************
Question: `q005. Is the operation * of standard multiplication on the set {-1, 1} a group. Note that the operation does have the property of associativity.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The operation is closed and has identity and inverse properties
3
Ok
*********************************************
Question: `q006. We've referred to the property of associativity, but we haven't yet defined it. Associativity essentially means that when an operation (technically a binary operation, but don't worry about that a terminology at this point) is performed on three elements of a set, for example a + b + c, it doesn't matter whether we first perform a + b then add c, calculating (a + b) + c, or group the b and c so we calculate a + (b + c).
If + means addition on real numbers, show that (3 + 4) + 5 = 3 + ( 4 + 5).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
3 + 4) + 5 = 7 + 5 = 12.
3 + ( 4 + 5) = 3 + 9 = 12.
Either way we do the calculation we get the same thing
2
Ok
*********************************************
Question: `q007. Verify that for the operation @ defined on {0, 1, 2} by x @ y = remainder when x * y is double then divided by 3, we have 2 @ (0 @ 1) = ( 2 @ 0 ) @ 1.
Verify also that (2 @ 1) @ 1 = 2 @ ( 1 @ 1).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
(2 @ 1) @ 1 = 2 @ ( 1 @ 1).
2
Ok
*********************************************
Question: `q008. Does the result of the preceding exercise prove that the @ operation is associative on the set {0, 1, 2}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
27
3
Ok
*********************************************
Question: `q009. Earlier we verified the properties of closure, identity and inverse for the multiplication operation * on the set {-1, 1}. We asserted that this operation was associative, so that this set with this operation forms a group.
It would still be too time-consuming to prove that * is associative on {-1, 1}, but list the possible combinations of a, b, c from the set and verify associativity for any three of them.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
a, b, c) = (-1, -1, -1) or (-1, -1, 1) or (-1, 1, -1) or (-1, 1, 1) or (1, -1, -1) or (1, -1, 1) or (1, 1, -1)
2
Ok
"
&#I need to see the questions so I can be sure what your answers mean. Most of the time I can tell, but I'm dealing with information that comes in from over 1000 different files, containing a total of about 10 000 questions. While I'm familiar with the content and sequencing of the questions, having written them all, and know what I'm looking for, different students will answer these questions in different ways and I need to be able to relate your answers to the specific wording of each question.
When reviewing my responses you will also need to be able to relate your answers and my comments to the specifics of the original document.
So it will be important for you on future documents to insert your responses into a copy of the original document, according to instructions, without otherwise changing any of the content of the original document.
This will ensure you of the best possible feedback on your work. &#
#$&*
#$&*
course Mth 151
7/27 11
Question: `q001. There are nine questions in this assignment.A group is a set and an operation on that set which has the properties of closure, associativity, identity and inverse. The set {1, 2} on the operation @ of Assignment 21, defined by x @ y = remainder when the product x * y is divided by 3, does have the associative property. Is the set {1, 2} a group on @?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Yes the set is a group
2
Ok
*********************************************
Question: `q002. Which of the properties closure, identity, commutativity, inverse, does the standard addition operation + have on the set {-1, 0, 1}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Commutative
2
Ok
*********************************************
Question: `q003. Does the operation * of standard multiplication on the set {-1, 0, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
Ok
*********************************************
Question: `q004. Does the operation * of standard multiplication on the set {-1, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
ok
*********************************************
Question: `q005. Is the operation * of standard multiplication on the set {-1, 1} a group. Note that the operation does have the property of associativity.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The operation is closed and has identity and inverse properties
3
Ok
*********************************************
Question: `q006. We've referred to the property of associativity, but we haven't yet defined it. Associativity essentially means that when an operation (technically a binary operation, but don't worry about that a terminology at this point) is performed on three elements of a set, for example a + b + c, it doesn't matter whether we first perform a + b then add c, calculating (a + b) + c, or group the b and c so we calculate a + (b + c).
If + means addition on real numbers, show that (3 + 4) + 5 = 3 + ( 4 + 5).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
3 + 4) + 5 = 7 + 5 = 12.
3 + ( 4 + 5) = 3 + 9 = 12.
Either way we do the calculation we get the same thing
2
Ok
*********************************************
Question: `q007. Verify that for the operation @ defined on {0, 1, 2} by x @ y = remainder when x * y is double then divided by 3, we have 2 @ (0 @ 1) = ( 2 @ 0 ) @ 1.
Verify also that (2 @ 1) @ 1 = 2 @ ( 1 @ 1).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
(2 @ 1) @ 1 = 2 @ ( 1 @ 1).
2
Ok
*********************************************
Question: `q008. Does the result of the preceding exercise prove that the @ operation is associative on the set {0, 1, 2}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
27
3
Ok
*********************************************
Question: `q009. Earlier we verified the properties of closure, identity and inverse for the multiplication operation * on the set {-1, 1}. We asserted that this operation was associative, so that this set with this operation forms a group.
It would still be too time-consuming to prove that * is associative on {-1, 1}, but list the possible combinations of a, b, c from the set and verify associativity for any three of them.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
a, b, c) = (-1, -1, -1) or (-1, -1, 1) or (-1, 1, -1) or (-1, 1, 1) or (1, -1, -1) or (1, -1, 1) or (1, 1, -1)
2
Ok
"
&#I need to see the questions so I can be sure what your answers mean. Most of the time I can tell, but I'm dealing with information that comes in from over 1000 different files, containing a total of about 10 000 questions. While I'm familiar with the content and sequencing of the questions, having written them all, and know what I'm looking for, different students will answer these questions in different ways and I need to be able to relate your answers to the specific wording of each question.
When reviewing my responses you will also need to be able to relate your answers and my comments to the specifics of the original document.
So it will be important for you on future documents to insert your responses into a copy of the original document, according to instructions, without otherwise changing any of the content of the original document.
This will ensure you of the best possible feedback on your work. &#
#$&*
#$&*
course Mth 151
7/27 11
Question: `q001. There are nine questions in this assignment.A group is a set and an operation on that set which has the properties of closure, associativity, identity and inverse. The set {1, 2} on the operation @ of Assignment 21, defined by x @ y = remainder when the product x * y is divided by 3, does have the associative property. Is the set {1, 2} a group on @?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Yes the set is a group
2
Ok
*********************************************
Question: `q002. Which of the properties closure, identity, commutativity, inverse, does the standard addition operation + have on the set {-1, 0, 1}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Commutative
2
Ok
*********************************************
Question: `q003. Does the operation * of standard multiplication on the set {-1, 0, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
Ok
*********************************************
Question: `q004. Does the operation * of standard multiplication on the set {-1, 1} have the properties of closure, identity and inverse?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Inverse
2
ok
*********************************************
Question: `q005. Is the operation * of standard multiplication on the set {-1, 1} a group. Note that the operation does have the property of associativity.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The operation is closed and has identity and inverse properties
3
Ok
*********************************************
Question: `q006. We've referred to the property of associativity, but we haven't yet defined it. Associativity essentially means that when an operation (technically a binary operation, but don't worry about that a terminology at this point) is performed on three elements of a set, for example a + b + c, it doesn't matter whether we first perform a + b then add c, calculating (a + b) + c, or group the b and c so we calculate a + (b + c).
If + means addition on real numbers, show that (3 + 4) + 5 = 3 + ( 4 + 5).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
3 + 4) + 5 = 7 + 5 = 12.
3 + ( 4 + 5) = 3 + 9 = 12.
Either way we do the calculation we get the same thing
2
Ok
*********************************************
Question: `q007. Verify that for the operation @ defined on {0, 1, 2} by x @ y = remainder when x * y is double then divided by 3, we have 2 @ (0 @ 1) = ( 2 @ 0 ) @ 1.
Verify also that (2 @ 1) @ 1 = 2 @ ( 1 @ 1).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
(2 @ 1) @ 1 = 2 @ ( 1 @ 1).
2
Ok
*********************************************
Question: `q008. Does the result of the preceding exercise prove that the @ operation is associative on the set {0, 1, 2}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
27
3
Ok
*********************************************
Question: `q009. Earlier we verified the properties of closure, identity and inverse for the multiplication operation * on the set {-1, 1}. We asserted that this operation was associative, so that this set with this operation forms a group.
It would still be too time-consuming to prove that * is associative on {-1, 1}, but list the possible combinations of a, b, c from the set and verify associativity for any three of them.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
a, b, c) = (-1, -1, -1) or (-1, -1, 1) or (-1, 1, -1) or (-1, 1, 1) or (1, -1, -1) or (1, -1, 1) or (1, 1, -1)
2
Ok
"
&#I need to see the questions so I can be sure what your answers mean. Most of the time I can tell, but I'm dealing with information that comes in from over 1000 different files, containing a total of about 10 000 questions. While I'm familiar with the content and sequencing of the questions, having written them all, and know what I'm looking for, different students will answer these questions in different ways and I need to be able to relate your answers to the specific wording of each question.
When reviewing my responses you will also need to be able to relate your answers and my comments to the specifics of the original document.
So it will be important for you on future documents to insert your responses into a copy of the original document, according to instructions, without otherwise changing any of the content of the original document.
This will ensure you of the best possible feedback on your work. &#
#$&*