The simplified switching circuit for the following circuit is

Step-by-step solution

Let p, q, r represent the switches S₁, S₂, S₃ respectively. The Boolean expression for the top branch is p (q r) . The Boolean expression for the bottom branch is r q p , which can be rewritten as p ( q r) . The total circuit is the parallel combination of these two branches, so the expression is: [p (q r)] [p ( q r)] Using De Morgan's Law, q r (q r) . Substituting this, we get: [p (q r)] [p (q r)] Using the distributive law, we can factor out p : p [(q r) (q r)] Since A A T (where T represents a closed circuit or