The set of all positive integers ($\mathbb{Z}^{+}$) = { 1, 2, 3, 4, 5, 6…...}
A set A under a binary operation * can be called as a group G iff it satisfies
Closure property
Associativity
Identity property
Inverse property
Here the set contains an identity element which is 1….But the set doesn’t hold inverse property
Eg: for element 2, we cannot find an inverse such that when we multiply any element of the set A (positive
integers) we get the identity element 1...
Hence it cannot be a Group…
It is a Monoid (A,*) since the set A under multiplication satisfies Closure, Associative and Identity property….
Since it also satisfies Commutative property , it can be called a Abelian Monoid...
The best option would be B...