Construct the Simplified Circuit for the Following Circuit - Mathematics and Statistics

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Construct the simplified circuit for the following circuit:

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Solution

Let p : switch S1 is closed
     q : switch S2 is closed
      r : switch S3 is closed
  ~ p : switch S1 is open
  ~ q : switch S2 is open
   ~ r : switch S3 is open
The symbolic form of the given circuit
[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p] 
= p ∧ [(q ∨ r) ∨ (~ q ∧ ~ r) ….(Distributive law)
= p ∧ [(q ∨ r) ∨ ~ (q  r)] ….(De Morgan’s law)
= p ∧ T ….(Compliment law)
= p ….(Identity law)
The new simplified circuit is

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2014-2015 (October)

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