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(1) For each of the following assertions, if it is valid, find a form.pdf

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(1) For each of the following assertions, if it is valid, find a formal proof, in the system discussed in lecture - to emphasize, you can only use the rules of inference given in lecture and the macros aboveand if it is not valid, find a counterexample (i.e. true/false assignments to the variables which make the assumptions true but the conclusion false). \begin{tabular}{l} PQ \\ (PQ)R \\ \hlineR \end{tabular} (a) (b) (c) \begin{tabular}{|l|} \hlineXY \\ XZ \\ \hlineZY \\ \hline \hlineEF \\ GF \\ HI \\ EH \\ \hlineGI \\ \hline \hline \end{tabular} (d) LM(MN)(LK)P(QL)PK (e) PQR(ST)R(PT)RQS (f) A(BC)CA(DA)CDB.

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(1) For each of the following assertions, if it is valid, find a formal proof, in the system discussed in lecture - to emphasize, you can only use the rules of inference given in lecture and the macros aboveand if it is not valid, find a counterexample (i.e. true/false assignments to the variables which make the assumptions true but the conclusion false). begin{tabular}{l} PQ (PQ)R hlineR end{tabular} (a) (b) (c) begin{tabular}{|l|} hlineXY XZ hlineZY hline hlineEF GF HI EH hlineGI hline hline end{tabular} (d) LM(MN)(LK)P(QL)PK (e) PQR(ST)R(PT)RQS (f) A(BC)CA(DA)CDB

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