If the truth value of the statement pattern [ p r ] r q is False, then which of the following has truth value False?

Step-by-step solution

Given the statement S = [p r] ( r q) with truth value False, determine which of the provided options also evaluates to False. An implication A B is false only when A is true and B is false. Therefore: p r must be true, which requires both p and r to be true, so p T and r F . Since r q must be false and r T , it follows that T q is false only if q F . Truth values: p T , q F , r F . Evaluating the options: Option A: (p r) r becomes (T F) T , which simplifies to T T and is true. Option B: (r q) p becomes (F F) F , or