If the symbolic form of the switching circuit is $[\sim \mathrm{pv}(\mathrm{p} \wedge \sim \mathrm{q})]…

If the symbolic form of the switching circuit is $[\sim \mathrm{pv}(\mathrm{p} \wedge \sim \mathrm{q})] \mathrm{v} \mathrm{q}$, then the current flows through the circuit onlyif
  1. irrespective of status of the switches
  2. one switch should be open and other should be closed
  3. both switches should be closed
  4. both switches should be open

Solution

$[\sim p \vee(p \wedge \sim q)] \vee q$ $=[(\sim p \vee p) \wedge(\sim p \vee \sim q)] \vee q$ $E[T \wedge(\sim p \vee \sim q)] \vee q$ $\equiv(\sim p \vee \sim q) \vee q$ $\equiv \sim p \vee(\sim q \vee q) \equiv \sim p \vee T \equiv T$ This shows that current flows irrespective of status of the switches.

Asked in: MHT CET 2020 (14 Oct Shift 2)

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