If x * y = x + y + xy then (G, *) is _____________(a) Monoid(b) Abelian group(c) Commutative semigroup(d) Cyclic groupThe question was posed to me at a job interview.This is a very interesting question from Group Axioms topic in chapter Groups of Discrete Mathematics

If x * y = x + y + xy then (G, *) is _____________(a) Monoid(b) Abelia

1.	If x * y = x + y + xy then (G, *) is _____________(a) Monoid(b) Abelian group(c) Commutative semigroup(d) Cyclic groupThe question was posed to me at a job interview.This is a very interesting question from Group Axioms topic in chapter Groups of Discrete Mathematics
Answer» Right choice is (c) COMMUTATIVE semigroup The explanation: LET x and y belongs to a GROUP G.Here closure and associativity axiom holds simultaneously. Let e be an element in G such that x * e = x then x+e+xe=a => e(1+x)=0 => e = 0/(1+x) = 0. So, identity axiom does not exist but commutative PROPERTY holds. THUS, (G,*) is a commutative semigroup.

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