If the truth value of the compound statement [(p q) (q r) r] (p q) is false, then the truth values of the statement patterns (p q) (q r) and (p r) (q p) are, respectively ...

Step-by-step solution

The given compound statement is [(p q) (q r) r] (p q) . An implication X Y is false if and only if X is true and Y is false. Thus, (p q) (q r) r is true and p q is false. For the conjunction (p q) (q r) r to be true, each of its components must be true: r is true r = F q r is true q F is true q = F p q is true p F is true p = F Checking the second part with these values: p q = F T = F , which satisfies the condition that Y is false. So, the truth values are p = F , q = F , r = F . Now, evaluating the first statemen