Answer:
Step-by-step explanation:
Given that *is the binary operation in the sets of integers.
[tex]a*b = a - b + ab[/tex]
closure: a-b+ab is again an integer belongs to Z. Hence closure is true.
Associativity: [tex]a*(b*c) = a*(b+c-bc)\\= a-b-c+bc+ab+ac-abc\\= a-b-c +ab+bc+ca-abc[/tex]
[tex](a*b)*c=(a+b-ab)*c\\=a+b-ab-c+ac+bc-abc\\[/tex]
The two are not equal. Hence this cannot be a group as associtiavity does not hold good.
