The logically equivalent statement of ( p q) ( p q) (p q) is

Step-by-step solution

Given statement: S = ( p q) ( p q) (p q) Factoring out p from the first two terms using the distributive law gives: p (q q) (p q) Since q q is a tautology and p T p by the identity law, we obtain: p (p q) Distributing the disjunction: ( p p) ( p q) The complement p p simplifies to T , and T ( p q) reduces to p q . The simplified expression p q corresponds to option B . Final answer: B