Question

Construct the switching circuit for the following logical statement:

(p ∨ ∼ q) ∨ (q ∧ r). Also construct the switching circuit for its simplified form.

Answer 1

Let p: The switch S₁

q: The switch S₂

r: The switch S₃

The switching circuit:

Now (p ∨ ∼ q) ∨ (q ∧ r)

= p ∨ [∼ q ∨ (q ∧ r)]      ....(Associative law)

= p v [(∼q ∨ q) ∧ (∼ q ∨ r)]   ....(Distributive law)

= p v [T ∧ (∼ q ∨ r)]    ....(Complement law)

= p v [(∼ q v r)]     .....(Identity law)

The simplified switching circuit is: