assignments 26

course Mth 151

assignment 27 was the end of program. unable to run 27,28,29,30.

z?????????}assignment #026

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026. Modular systems

Liberal Arts Mathematics I

12-14-2007

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00:42:38

`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).

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RESPONSE -->

3*9 mod 4 is the remainder when 3*9 is divid. by 4. 3*9=27 and 27/4 leaves a remainder of 3. 3*9mod 4= 3

7*12 mod4 is the remainder when 7*12 is divd. by 4. 7*12 =84 and 84/4 leaves a reamainder 0. 7*12 mod 4=0

11*13 mod4 is the remainder when 11*13 is divded by 4. 11*13=143 and 143/4 leaves a remainder3, we see that 11*13 mode 4=3

confidence assessment: 2

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00:50:28

`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.

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RESPONSE -->

x is 1

the operation is closed

its associative it has commutativy property

* 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

confidence assessment: 2

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00:54:27

`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.

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RESPONSE -->

the operation is closed and has identity 1.

2*3 mod 5=6, 6/5 r1

3*4 mode 5=12, 12/5 r2

2*4 mod 5=8, 8/5 r3

* 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

confidence assessment: 3

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00:55:36

`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?

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RESPONSE -->

x=4 is a solution to the equation, 3x+7=9 mod5

confidence assessment: 2

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00:56:58

`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?

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RESPONSE -->

3x+7=9 mod5 is equivalent to 3x-2=0 mode

x=9

confidence assessment: 2

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00:58:21

`q006. What are the first five positive values of x which solve the equation 3x + 7 = 9 (mod 5) of the preceding problem?

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RESPONSE -->

x=4,9,14,19,and 24

confidence assessment: 1

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"

This looks good.