I. Implement the following combinational circuit with a multiplexer.

$1.$ A stop signal, S $,$ is to be generated in a simple copy machine to halt operation and activate an indicator light whenever either of the following conditions is present:

$(1)$ The absence of paper in the feeder tray; or

$(2)$ Activation of the two microswitches in the paper path, indicating a paper jam.

The presence of paper in the feeder tray is signaled by a HIGH at logic signal P$.$ Each microswitch generates a logic signal $($ Q and R $)$ that transitions to HIGH when paper passes over the switch, thereby activating it$.$ Design a combinational circuit that generates a HIGH output signal S under the specified conditions.

$2.$ Design a combinational circuit that manages the operation of an elevator door in a three$-$story building. The circuit comprises four inputs. M represents a logic signal that denotes the operational status of the elevator, with $\backslash (\backslash$mathrm$\{$M$\}=1\backslash )$ indicating movement and M $\backslash (=0\backslash )$ indicating a stationary state. F$1,$ F$2,$ and F$3$ serve as floor indicator signals that typically maintain a LOW state, transitioning to HIGH exclusively when the elevator aligns with the respective floor level. When the elevator aligns with the second floor, F$2$ equals $1,$ while F$1$ and F$3$ equal $0.$ The circuit output is the OPEN signal, which is typically LOW and transitions to HIGH when the elevator door is to be opened.