Let p : the switch S1 is closed
q : the switch S2 is closed
r : the switch S3 is closed
~ q : the switch S2' is closed or the switch S2 is open
~ r : the switch S3' is closed or the switch S3 is open.
Then,
The symbolic form of the given switching circuit is :
[p ∨ (~ q) ∨ (~ 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 S1.
The simplified form of the given circuit is :