Question
Write the symbolic form of the following switching circuits construct its switching table and interpret it.
✓
Answer
Let $p :$ the switch $S_1$ is closed
$q :$ the switch $S_2$ is closed
$\sim p :$ the switch $S_1‘$ is closed or the switch $S_1$ is open
$\sim q :$ the switch $S_2‘$ is closed or the switch $S_2$ is open.
Then the symbolic form of the given circuit is :
$(p ∨ \sim q) ∨ (\sim p ∧ q)$
Since the final column contains all’ $1′,$ the lamp will always glow irrespective of the status of switches.
$q :$ the switch $S_2$ is closed
$\sim p :$ the switch $S_1‘$ is closed or the switch $S_1$ is open
$\sim q :$ the switch $S_2‘$ is closed or the switch $S_2$ is open.
Then the symbolic form of the given circuit is :
$(p ∨ \sim q) ∨ (\sim p ∧ q)$
Since the final column contains all’ $1′,$ the lamp will always glow irrespective of the status of switches.
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