0 votes 0 votes Which of the following true about (R,*)? 1) Group but not commutative 2) A commutative group 3) Not a semigroup 4) Not a monoid Set Theory & Algebra set-theory&algebra group-theory + – Mahesha999 asked Jan 24, 2015 • recategorized Jul 18, 2016 by LeenSharma Mahesha999 1.6k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 4 votes 4 votes Its a monoid. Closure, associativity, Identity are defined for Real numbers.But inverse is not defined as R can be zero also. So (R,*) is neither Group nor Abelian(commutative), but Monoid. GateMaster Prime answered Jan 25, 2015 • selected Jan 27, 2015 by Mahesha999 GateMaster Prime comment Share Follow See all 3 Comments See all 3 3 Comments reply Arjun commented Jan 25, 2015 reply Follow Share So, all options are wrong? 0 votes 0 votes GateMaster Prime commented Jan 26, 2015 reply Follow Share To mark one option among these, i will go with the best choice , i.e. option 3). Because its a Monoid, although it is also A Semigroup. 0 votes 0 votes akash.dinkar12 commented Aug 7, 2018 reply Follow Share But option A is saying that Not a semigroup. So None of these options would be correct. 0 votes 0 votes Please log in or register to add a comment.