#$&*
course mth 151
8/4
Question: `q001. There are six questions in this assignment.We defined an operation as follows: x * y (mod 4) = remainder when x * y is divided by 4. Find 3 * 9 (mod 4); 7 * 12 (mod 4) and 11 * 13 (mod 4).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
3 * 9 (mod 4) = 3
7 * 12 (mod 4) = 0
11 * 13 (mod 4) = 3
3
Ok
*********************************************
Question: `q002. Make a table for the x * y mod 4 operation, which we will call '* mod 4', operating on the set {0, 1, 2, 3}.
Determine which of the properties, including commutativity, associative, identity, inverse and closure properties, are properties of this operation.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The table for this operation is therefore
* mod 4 0 1 2 3
0 0 0 0 0
1 0 1 2 3
2 0 2 0 2
3 0 3 2 1
closed, since the remainder upon dividing by 4 must always be 0, 1, 2 or 3 and hence in the set {0, 1, 2, 3}
3
Ok
*********************************************
Question: `q003. Repeat the preceding exercise for the operation x * y mod 5, defined to give the remainder when x * y is divided by 5, on the set {1, 2, 3, 4}. Determine which of the properties are exhibited by this operation.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
* mod 5 1 2 3 4
1 1 2 3 4
2 2 4 1 3
3 3 1 4 2
4 4 3 2 1
inverse property
3
Ok
*********************************************
Question: `q004. The equation 3x + 7 = 9 (mod 5) has an integer solution for x = 0, 1, 2, 3 or 4. Which value of x is a solution to this equation?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Thus x = 4 is a solution to the equation 3x + 7 = 9 (mod 5)
3
Ok
*********************************************
Question: `q005. You see that x = 4 is a solution to the equation 3x + 7 = 9 (mod 5). One of the numbers x = 5, 6, 7, 8, 9 is also a solution. Which one is it?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
x = 9 is our next solution
3
Ok
*********************************************
Question: `q006. What are the first five positive values of x which solve the equation 3x + 7 = 9 (mod 5) of the preceding problem?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
x = 4, 9, 14, 19 and 24
3
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. &#
#$&*