MHTCET 26 Apr 2025 Shift 1 Paper

Concept:In a switching circuit, switches in series represent AND $(\wedge)$, and switches in parallel represent OR $(\vee)$.The given circuit is simplified using Boolean algebra laws.Explanation:The logical expression for the given circuit is:$$[(\sim p \wedge \sim q) \vee p \vee q] \wedge r \wedge [(p \wedge q) \vee (\sim p \wedge q)]$$First simplify the bracket $(\sim p \wedge \sim q) \vee p \vee q$.By De Morgan's law, $\sim p \wedge \sim q = \sim(p \vee q)$.So, $\sim(p \vee q) \vee (p \vee q) = T$ (Complement law).Now simplify $(p \wedge q) \vee (\sim p \wedge q)$.Taking $q$ common: $q \wedge (p \vee \sim p) = q \wedge T = q$.Therefore, the whole expression becomes:$$T \wedge r \wedge q = q \wedge r$$Thus, the circuit is equivalent to switch $S_2$ and switch $S_3$ connected in series.Answer:The simplified logical statement is $q \wedge r$.The simplified equivalent circuit has $S_2$ and $S_3$ in series.