Closure? Yes.
If you take two integers, the maximum out of the two would be one of these two. Means an integer.
Associativity. Yes
Position of the sequence doesn't matter.
Example: Maximum of a and b then c $\equiv$ Maximum of b and c then a
Identity?
We need an e, such that $x*e=x$ $=>$ $max(x,e)=x$
So, e must be the smallest negative integer. Which is $-∞$; which actually is just an abstraction. There's no defined number that represents $-∞$
So, identity doesn't exist.
Hence, the given structure is a Semi Group. Option D