Q.Construct the switching circuit of the following: $[(p \wedge r) \vee (\sim q \wedge \sim r)] \wedge (\sim p \wedge \sim r)$

The expression is $[(p \wedge r) \vee (\sim q \wedge \sim r)] \wedge (\sim p \wedge \sim r)$. The OUTERMOST connective is $\wedge$ (between the bracket and $(\sim p \wedge \sim r)$), so the circuit splits into two series blocks.

Left block: $(p \wedge r) \vee (\sim q \wedge \sim r)$ — a disjunction, so it is a parallel combination of {switches $p,r$ in series} and {switches $\sim q, \sim r$ in series}.

Right block: $\sim p \wedge \sim r$ — switches $\sim p$ and $\sim r$ in series. …

Identify the outermost connective first (here $\wedge$) to decide series vs parallel at the …

Reading left-to-right and wiring everything in parallel because the first inner operator seen is $\vee$, instead of …