assignments 21

course Mth 151

for some reason i couldnt get assignment 20 to run!!

assignment 21 22:19:28`q001. If we define the operation @ on two numbers x and y by

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x @ y = remainder when the product x * y is multiplied by 2 then divided by 3, then find the following:

2 @ 5,

3 @ 8,

7 @ 13.

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RESPONSE -->

2 @ 5,

3 @ 8,

7 @ 13

2 @ 5=2*5=10

10=20

20/3=6 2r

2@5=2

3 @ 8=3*8=24

24=48

48/3=16

3@8=0

7 @ 13=7*13=91

91=182

182/3=60 2r

7@13=2

confidence assessment: 3

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22:22:21

`q002. If we define the @ operation from the previous exercise just on the set {5, 6, 7} , we can use the same process as in the preceding solution to get 5 @ 5 = 2, 5 @ 6 = 0, 5 @ 7 = 1, 6 @ 5 = 0, 6 @ 6 = 0, 6 @ 7 = 0, 7 @ 5 = 1, 7 @ 6 = 0 and 7 @ 7 = 2. We can put these results in a table as follows:

@ 5 6 7

5 2 0 1

6 0 0 0

7 1 0 2.

Make a table for the @ operation restricting x and y to the set {2, 3, 4}.

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RESPONSE -->

table : @ ( 2, 3, 4 )

2 2 0 1

3 0 0 0

4 1 0 2

confidence assessment: 2

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22:24:35

`q003. All the x and y values for the table in the preceding problem came from the set {2, 3, 4}. From what set are the results x @ y taken?

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RESPONSE -->

Operation x@y consit of a remainder when it is divided by 3

confidence assessment: 1

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22:26:15

`q004. Are the results of the operation x @ y on the set {2, 3, 4} all members of the set {2, 3, 4}?

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RESPONSE -->

@ 2 3 4

2 1 0 2

3 0 0 0

4 2 0 1

confidence assessment: 2

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22:32:31

`q005. Since the operation x @ y on the set {2, 3, 4} can result in at least some numbers which are not members of the set, we say that the @operation is not closed on the set {2, 3, 4}.

Is the @ operation closed on the set S = {0, 1, 2}? Is the @ operation closed on the set T = {0, 2}? Is the @ operation closed on the set R = {1, 2}?

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RESPONSE -->

s=0,1,2- closed

the operation gives one of the div. by 3, a remainder of 0,1,2

t=0,2-closed

the operation of all results 0&2.

r=1,2- closed

all results are 1,2

confidence assessment: 1

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22:34:55

`q006. How can we tell by looking at the table whether the operation is closed?

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RESPONSE -->

All the #s come from the left column under the @ in a table.

confidence assessment: 1

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22:35:47

`q007. When calculating x @ y for two numbers x and y, does it make a difference whether we calculate x @ y or y @ x?

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RESPONSE -->

they are both the same: x*y or y*x

confidence assessment: 2

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22:37:27

`q008. Does the operation of subtraction of whole numbers have the commutative property?

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RESPONSE -->

not true x-y=y-x

sub. of a whole #s doesnt have commutative property.

confidence assessment: 2

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22:37:52

`q009. Is the operation of subtraction closed on the set of whole numbers?

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RESPONSE -->

not closed

confidence assessment: 2

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22:39:01

`q010. Is the operation of addition closed and commutative on the set of whole numbers?

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RESPONSE -->

they can be added either way

x+y OR y+x

confidence assessment: 3

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22:40:03

`q011. When we multiply a number by 1, what must be our result?

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RESPONSE -->

the # 1 mult. by a another # is that #.

confidence assessment: 3

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22:42:02

`q012. A number which does not change any number with which it is combined using a certain operation is called the identity for the operation. As we saw in the preceding exercise, the number 1 is the identity for the operation of multiplication on real numbers.

Does the operation @ (which was defined in preceding exercises by x @ y = remainder when x * y is doubled and divided by 3) have an identity on the set {0, 1, 2}? Does @ have an identity on the set {0, 2}?

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RESPONSE -->

2 is the identity

@ 0 2 1

0 0 0 0

2 0 2 1

1 0 1 2

confidence assessment: 2

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22:43:33

`q013. Does the set of whole numbers on the operation of addition have an identity?

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RESPONSE -->

0 is the identity for addition on the set of a whole number

confidence assessment: 1

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22:51:08"

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