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 $: p ∨ (\sim p ∧ \sim q) ∨ (p ∧ q)$
Since the final column contains $‘0’$ when $p$ is $0$ and $q$ is $‘1’$, otherwise it contains $‘1′.$
Hence, the lamp will not glow when $S_1$ is OFF and $S_2$ is ON, otherwise the lamp will glow.
$q :$ 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 $: p ∨ (\sim p ∧ \sim q) ∨ (p ∧ q)$
Since the final column contains $‘0’$ when $p$ is $0$ and $q$ is $‘1’$, otherwise it contains $‘1′.$
Hence, the lamp will not glow when $S_1$ is OFF and $S_2$ is ON, otherwise the lamp will glow.
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