THE GATEBOOK

Normalization Lectures

For a positive number c, consider the open interval of real numbers. For , define

Which one of the following statements is true?

(A).G is monoid but not group

(B).G is a group but not abelian

(C).G is semigroup but not a monoid

(D).G is an abelian group

Let,

Therefore, is an Abelian Group. Also, the identity element in is ; and the inverse of an element is .