In Exercises 13-24, use propositional logic to prove that the argument is valid. 24. [A(BC)]C(AB) TABLE 1.11 Equivalence Rules \begin{tabular}{l|l|l} \hline Expression & Equivalent to & Name/Abbreviation for Rule \\ \hlinePQ & QP & Commutative-comm \\ PQ & QP & \\ \hline(PQ)R & P(QR) & Associative-ass \\ (PQ)R & P(QR) & \\ \hline(PQ) & PQ & De Morgan's Laws-De \\ (PQ) & PQ & Morgan \\ \hlinePQ & PQ & Implication-imp \\ \hlineP & (P) & Double negation-dn \\ \hlinePQ & (PQ)(QP) & Definition of equivalence-equ \end{tabular} TABLE 1.12 Inference Rules \begin{tabular}{l|l|l} \hline From & Can Derive & Name/Abbreviation for Rule \\ \hlineP,PQ & Q & Modus ponens-mp \\ \hlinePQ,Q & P & Modus tollens-mt \\ \hlineP,Q & PQ & Conjunction-con \\ \hlinePQ & P,Q & Simplification-sim \\ \hlineP & PQ & Addition-add \end{tabular}