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Valentin [98]
3 years ago
10

Is the set \mathbb{Z} a group under the operation a*b = a - b + ab ? Justify your answer.

Mathematics
1 answer:
Daniel [21]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that *is the binary operation in the sets of integers.

a*b = a - b + ab

closure: a-b+ab is again an integer belongs to Z.  Hence closure is true.

Associativity: a*(b*c) = a*(b+c-bc)\\= a-b-c+bc+ab+ac-abc\\= a-b-c +ab+bc+ca-abc

(a*b)*c=(a+b-ab)*c\\=a+b-ab-c+ac+bc-abc\\

The two are not equal.  Hence this cannot be a group as associtiavity does not hold good.

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