Let p : The switch S1 is closed.
q : The switch S2 is closed.
r : The switch S3 is closed.
~p : The switch \(S'_1\) is closed or the switch S1 is open
~q : The switch \(S'_2\) is closed or the switch S2 is open
~r : The switch \(S'_3\) is closed or the switch S3 is open.
The symbolic form of the given circuit is
(p \(\lor\) ~q \(\lor\) ~r) \(\land\) [p \(\lor\) (q \(\land\) r)]
\(\therefore\)The switching table corresponding to the given statements is :
The final column of the above table is equivalent to the column of ‘p’ i.e. column corresponding to switch S1. Hence, the given circuit is equivalent to the circuit where only switch S1 is present. Hence,
switching circuit is as follows:
