DM-Groups and Lattice-Q8

+1 vote

(Q, *) is an algebraic structure where Q represents rational numbers and * denotes multiplication. Which one of the following statements is true?

(A).Q is an abelian group. 

(B).Q is a group but not abelian. 

(C).Q is a semigroup but not a monoid. 

(D).Q is monoid but not group.

asked Jul 8, 2019 in Discrete Maths by gbeditor (44,580 points)
reshown Jul 9, 2019 by gbeditor

1 Answer

0 votes
D is correct one
answered Jul 9, 2019 by (34,650 points)
@tsnikhilsharmagate2018 could you explain me the solution to this problem?
it is not a group because of element 0, for it to be a group 0 should have an inverse.
a*b=b*a=e (here e = 1)
when a = 0, we cant find 'b', such that 0*b = 1. So it is not a group.

it is already a semi-group as identity element (=1) exists. for every 'a', we can find a*e=e*a=a (just put e=1).

therefore it is a semi group but not a group