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

Step-by-step solution

Let X = (p q) (q r) ( r) and Y = p q . The truth value of X Y is given as False. An implication X Y is False if and only if X is True and Y is False. For X to be True, all its conjuncts must be True: 1) r is True r is False ( F ). 2) q r is True. Since r is False, q must be False ( F ). 3) p q is True. Since q is False, p must be True ( T ). Checking Y : p q = T F = F , which satisfies the condition that Y is False. Thus, the truth values are p = T , q = F , and r = F . Now, evaluating the required statements: p q