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Construct the simplified circuit for the following circuit:

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#### Solution

Let p : switch S_{1} is closed

q : switch S_{2} is closed

r : switch S_{3} is closed

~ p : switch S_{1} is open

~ q : switch S_{2} is open

~ r : switch S_{3} 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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