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in Algebra by (31.0k points)
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Represent the following switching circuit in symbolic form and construct its switching table. Write your conclusion from the switching table.

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Best answer

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 :

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