The correct simplified circuit diagram for the logical statement [ q ( q r ) p ( p r ) ] ( p r ) where p , q , r represent switches s ₁, ~s ₂, ~s ₃ respectively.

Step-by-step solution

The logical expression [q ( q r)] [ p (p r)] (p r) simplifies using distributive and identity laws. Applying the distributive law to q ( q r) yields (q q) (q r) , which simplifies to q r since q q is a contradiction. Similarly, p (p r) distributes to ( p p) ( p r) and reduces to p r as p p is a tautology. Substituting, the expression becomes [(q r) ( p r)] (p r) . Distributing (q r) ( p r) gives [(q r) p] [q (r r)] , where r r is false, simplifying to q r p . The expression is now (q r p) (p r) . Factoring out r re