Q.Express the following switching circuit in the symbolic form of logic. Construct the switching table and interpret it:

Let $p:$ switch $S_1$ is closed, $q:$ switch $S_2$ is closed. $S_1'$ closes exactly when $S_1$ is open (so $S_1'\equiv\sim p$), and $S_2'\equiv\sim q$. The upper/lower branches are in parallel (OR), then in series (AND) with $S_1'$ and $S_2'$ (also in series, AND).

Let $p:$ switch $S_1$ is closed (ON), $q:$ switch $S_2$ is closed (ON). The switch $S_1'$ is closed exactly when $S_1$ is open, so it corresponds to $\sim p$; similarly $S_2'$ corresponds to $\sim q$.

From the circuit: $S_1$ and $S_2$ are in parallel ($p\vee q$), and this combination is in series with $S_1'$ then $S_2'$ (also in series with each other): $(p\vee q)\wedge(\sim p)\wedge(\sim q)$.

Symbolic form: $s\equiv (p\vee q)\wedge\sim p\wedge\sim q$

Switching table: