Question
Give an alternative equivalent simple circuits for the following circuits :
✓
Answer
(i) Let p : the switch $\mathrm{S}_1$ is closed
$q$ : the switch $\mathrm{S}_2$ is closed
$\sim \mathrm{p}$ : the switch $\mathrm{S}_1{ }^{\prime}$ is closed or the switch Si is open Then the symbolic form of the given circuit is :
$p \wedge(\sim p \vee q) .$
Using the laws of logic, we have,
$p \wedge(\sim p \vee q) $
$ =(p \wedge \sim p) \vee(p \wedge q) \ldots(\text { By Distributive Law }) $
$ =F \vee(p \wedge q) \ldots(\text { By Complement Law })$
$ =p \wedge q \ldots \text { (By Identity Law) }$
Hence, the alternative equivalent simple circuit is :
$q$ : the switch $\mathrm{S}_2$ is closed
$\sim \mathrm{p}$ : the switch $\mathrm{S}_1{ }^{\prime}$ is closed or the switch Si is open Then the symbolic form of the given circuit is :
$p \wedge(\sim p \vee q) .$
Using the laws of logic, we have,
$p \wedge(\sim p \vee q) $
$ =(p \wedge \sim p) \vee(p \wedge q) \ldots(\text { By Distributive Law }) $
$ =F \vee(p \wedge q) \ldots(\text { By Complement Law })$
$ =p \wedge q \ldots \text { (By Identity Law) }$
Hence, the alternative equivalent simple circuit is :
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