The statement pattern [(p q) q] r is a tautology when r is equivalent to

Step-by-step solution

The statement pattern [(p q) q] r requires simplification to determine when it becomes a tautology. Since p q is logically equivalent to p q , the antecedent becomes ( p q) q . Applying the distributive law gives ( p q) (q q) . The term q q is always false, so the antecedent simplifies to p q . The original statement pattern is therefore equivalent to ( p q) r . For this to be a tautology, r must be true whenever p q is true—that is, when both p and q are false. Examining the options under p = F and q = F : p q eva