This is the template for DAM (discrete and argumentative mathematics).
We prove theorem $2.1$ using the method of proof by way of contradiction. This theorem states that for any set $A$, that in fact the empty set is a subset of $A$, that is $\emptyset \subset A$.
In this paper I demonstrate a novel design for an optoelectronic State Machine which replaces input/output forming logic found in conventional state machines with BDD based optical logic while still using solid state memory in the form of flip-flops in order to store states. This type of logic makes use of waveguides and ring resonators to create binary switches. These switches in turn can be used to create combinational logic which can be used as input/output forming logic for a state machine. Replacing conventional combinational logic with BDD based optical logic allows for a faster range of state machines that can certainly outperform conventional state machines as propagation delays within the logic described are in the order of picoseconds as opposed to nanoseconds in digital logic.