A monoid is called a group if _______
A. (a*a)=a=(a+c)
B. (a*c)=(a+c)
C. (a+c)=a
D. (a*c)=(c*a)=e
Answer:D
A monoid is called a group if _______
A. (a*a)=a=(a+c) B. (a*c)=(a+c) C. (a+c)=a D. (a*c)=(c*a)=e
Explanation: A monoid(B,*) is called Group if to each element there exists an element c such that (a*c)=(c*a)=e. Here e is called an identity element and c is defined as the inverse of the corresponding element.