Currently taking a logic class and trying to understand this.
You have two set $A$ and $B$.
Both sets are empty sets.
Is set $A$ a subset of the complement of set $B$?
Assume the context is the universal set.
The answer is yes. But there are several comments that need to be made:
The reason why $A$ is contained in the complement of $B$ is that $A$ (being the empty set) is a subset of any set. This is because we define "$A$ is contained in $C$" to mean that any element of $A$ is also an element of $C$. Now, since nothing is an element of $A$, this condition is satisfied in this case (one typically says that it is satisfied vacuously.)