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Abstract Algebra Page 15

1.2 Groups: Definition and Elementaryproperties

Examples

:

Note:




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Reversal Law

Problem

Theorem1.2.3 Cancellation Lawsof




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Proof

If possible x1 and x 2 are the solution of a*x =b.

Then a* x1 =b and a* x2 =b

Hence a* x1 = a* x2 implies x1 = x2 (By Left cancellation law)

Try the other yourself !

Problem




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Problem




SRIMAAN8072230063SRIM

AAN 8072

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63

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Problem

Problem

Binary operation:Properties:




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Examples




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(In the problem 4 the operation is +4, the addition modulo 4. a+4 b= r, the reminderobtained when a+b is divided by 4 )




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Problem

Problem




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Examples

Problem

Result:

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Problem

Problem

Problem




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Properties:

If an

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