Answer :

* is an operation as a*b = a+ b - ab where a, b Z. Let and b = 2 two integers.


So, * is a binary operation from .


For commutative,



Since a*b = b*a, hence * is a commutative binary operation.


Again for associative,


a*(b*c) = a*(b+ c- bc)


= a+ (b+ c- bc) -a (b+ c- bc)


= a+ b+ c- bc- ab- ac+ abc


(a*b) *c = (a+ b- ab) *c


= a+ b- ab+ c- (a+ b- ab) c


= a+ b+ c- ab- ac- bc+ abc


As a*(b*c) = (a*b) *c, hence * an associative binary operation.


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