Question
Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table.
✓
Answer
Let $p :$ the switch $S_1$ is closed
$q :$ the switch $S_2$ is closed
$r :$ the switch $S_3$ is closed
$\sim q :$ the switch $S_2‘$ is closed or the switch $S_2$ is open
$\sim r :$ the switch $S_3‘$ is closed or the switch $S_3$ is open.
Then, the symbolic form of the given switching circuit is : $[p ∨ (\sim q) ∨ (\sim r)] ∧ [p ∨ (q ∧ r)]$
From the table, the’ final column’ and the column of $p$ are identical. Hence, the given circuit is equivalent to the simple circuit with only one switch $S_1.$
the simplified form of the given circuit is :
$q :$ the switch $S_2$ is closed
$r :$ the switch $S_3$ is closed
$\sim q :$ the switch $S_2‘$ is closed or the switch $S_2$ is open
$\sim r :$ the switch $S_3‘$ is closed or the switch $S_3$ is open.
Then, the symbolic form of the given switching circuit is : $[p ∨ (\sim q) ∨ (\sim r)] ∧ [p ∨ (q ∧ r)]$
From the table, the’ final column’ and the column of $p$ are identical. Hence, the given circuit is equivalent to the simple circuit with only one switch $S_1.$
the simplified form of the given circuit is :
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