0 votes 0 votes A set of odd integers under the operation of multiplication forms A) A group but not abelian group B) A monoid but not group C) Semigroup but not monoid D) Abelian group Set Theory & Algebra group-theory discrete-mathematics + – srestha asked Dec 28, 2017 srestha 1.7k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Ashwin Kulkarni commented Dec 28, 2017 reply Follow Share B) It is monoid but not a group. Becuase inverse of an integer doesn't exist in this set. i.e. a * a-1 =1 3 * 1/3 = 1 but 1/3 doesn't exist. 2 votes 2 votes joshi_nitish commented Dec 28, 2017 reply Follow Share it will be monoid but not a group, above set is closed, associative and has an identity element e=1, but no element except {-1,1} has an inverse in above set under multiplication operation, so it is not group 0 votes 0 votes Anu007 commented Dec 28, 2017 reply Follow Share Closed = Groupoid Associative = Semi group Identity = Monoid Inverse = Group Commutative = Abelien 1 votes 1 votes Ashwin Kulkarni commented Dec 28, 2017 reply Follow Share I was about to ask, what is name of set if it is just closed. Thanks @Anu007 I didn't knew the name "Groupoid" 1 votes 1 votes joshi_nitish commented Dec 28, 2017 reply Follow Share if it is just closed, it is also known as 'structure'.. 1 votes 1 votes gari commented Dec 28, 2017 reply Follow Share Closed - Algebric structure, Groupoid, or closure property . 1 votes 1 votes Please log in or register to add a comment.