46 qa 2

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course Mth 151

11/26/12 846 pm

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

022. `query 22

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Question: `q4.6.9 {-1,0,1} group on multiplication?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

-1 0 1

-1 1 0 -1

0 0 0 0

1-1 0 1

This satisfies the identity property and it is a closed set.

It does not satisfy the inverse because zero doesn’t have an inverse in this case, so it is not a group.

confidence rating #$&*:

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3

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Given Solution:

`a** There are four criteria for the group: closure, identity, inverse property, and associativity.

The lack of any one of these properties means that the set and operation do not form a group.

The set is closed on multiplication.

The identity is the element that when multiplied by other elements does not change them. The identity for this operation is 1, since 1 * -1 = -1, 1 * 0 = 0 and 1 * 1 = 1.

Inverses are pairs of elements that give you 1 when you multiply them. For example -1 * -1 = 1 so -1 is its own inverse. 1 * 1 = 1 so 1 is also its own inverse. However, 0 does not have an inverse because there is nothing you can multiply by 0 to get 1.

Since there is an element without an inverse this is not a group. **

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Self-critique (if necessary):

ok

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Self-critique Rating:

3

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Question: `q4.6.25 verify (NT)R = N(TR)

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

(NT) R= N(TR)

(V) R=N(P)

m=m

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

3

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Given Solution:

`a** From the table

(NT)R= V R = M

and

N(TR)= N P = M

This verifies the identity. **

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Self-critique (if necessary):

ok

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Self-critique Rating:

3

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Question: `qquery 4.6.33 inverse of T

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

T is the inverse of T

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

3

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Given Solution:

`a** T is its own inverse because T T gives you the identity **

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Self-critique (if necessary):

ok

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Self-critique Rating:

3

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Question: `qquery 4.6.33 inverse of T

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

T is the inverse of T

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

3

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Given Solution:

`a** T is its own inverse because T T gives you the identity **

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Self-critique (if necessary):

ok

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Self-critique Rating:

#*&!

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