Can I solve my decision problem in $O(n)$ time?
I use set difference to find out if there are any elements in $s$ that don't exist in $A$. This should be $O(n)$ in the best cases if there is a good hash. Since I'm dealing with integers it should be $O(n)$ Explained here

I then use $len(s)$ and $len(A)$ which takes $O(1)$ time according to here.

A = [1,2,3,4,9]
s = [1,2,3,4,9]

elem_not_in_A = set(s) - set(A)

if len(s) &gt;= len(A):
    if len(elem_not_in_A) &gt; 0:
        output False
    else:
        output True
else:
    output False


If the set difference remains $O(n)$ and all the other statements remain $O(1)$ then yes it can be solved in $O(n)$ time.