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Quiz 1
Show that $(P \rightarrow Q) \rightarrow P) \wedge (\neg P)$ is unsatisfiable.
Solution: Construct a truth table: $$\begin{array}{l|l|l|l|l|l} P & Q & \neg P & P \rightarrow Q & (P \rightarrow Q) \rightarrow P & ((P \rightarrow Q) \rightarrow P) \wedge (\neg P) \\ \hline T & T & F & T & T & F\\ T & F & F & F & T & F\\ F & T & T & T & F & F\\ F & F & T & T & F & F\\ \end{array}$$ Since the column of the truth table corresponding to the formula $((P \rightarrow Q) \rightarrow P) \wedge (\neg P)$ is all falses, it follows that the formula is unsatisfiable.