The statement pattern [(p q) ( p r)] [( p r) (p q)] is

Step-by-step solution

Let A = p q and B = p r . The given statement pattern can be written as (A B) (B A) . Using the logical equivalence X Y X Y , the expression becomes: ( A B) ( B A) Using the commutative and associative properties of disjunction, we can rearrange the terms as: ( A A) ( B B) We know that for any statement X , X X T (where T represents a tautology). Substituting this into the expression, we get: T T T Therefore, the given statement pattern is a tautology. Answer: a tautology