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
$r$ : the switch $S_3$ is closed
$~q$ : the switch $S_2$‘ is closed or the switch $S_2$ is open
$~r$: the switch $S_3$‘ is closed or the switch $S_3$ is open.
Then the symbolic form of the given circuit is :$[p ∨ (~q) ∨ r)] ∧ [p ∨ (q ∧ r)]$
From the switching table, the ‘final column’ and the column of p are identical. Hence, the lamp will glow which $S_1$ is $‘ON’$.
$q$ : the switch $S_2$ is closed
$r$ : the switch $S_3$ is closed
$~q$ : the switch $S_2$‘ is closed or the switch $S_2$ is open
$~r$: the switch $S_3$‘ is closed or the switch $S_3$ is open.
Then the symbolic form of the given circuit is :$[p ∨ (~q) ∨ r)] ∧ [p ∨ (q ∧ r)]$
From the switching table, the ‘final column’ and the column of p are identical. Hence, the lamp will glow which $S_1$ is $‘ON’$.
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