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

The expression $(p \wedge q) \vee [\sim p \wedge (\sim q \vee p \vee r)]$ is a disjunction of two terms, so the overall circuit has two parallel branches.

Branch 1 is $p \wedge q$: switches $p$ and $q$ in series.

Branch 2 is $\sim p \wedge (\sim q \vee p \vee r)$: a series combination of switch $\sim p$ with the sub-circuit $(\sim q \vee p \vee r)$. Since $\sim q \vee p \vee r$ is a three-way disjunction, its three switches $\sim q$, $p$, and $r$ are all connected in parallel with one another, forming one parallel block; that block is then wired in series with switch $\sim p$. …

Work outside-in: outer ∨ gives the two main parallel branches; inside branch 2, the inner ∨ gives a …

Treating the inner three-switch disjunction as a chain rather than a single parallel block, o …