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Use the following premises to deduce $\neg P \vee Q$ in any way you wish: \\
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$\{1\}$&(1) $\neg W \rightarrow (\neg T \rightarrow (\neg P \vee S))$&Premise \\
$\{2\}$&(2) $\neg S \vee Q$&Premise \\
$\{3\}$&(3) $W \vee \neg T$&Premise \\
$\{4\}$&(4) $\neg W$&Premise \\
\hline 
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\textit{Solution:} \\
\begin{center}\begin{tabular}{|lll|}
\hline
$\{1\}$&(1) $\neg W \rightarrow (\neg T \rightarrow (\neg P \vee S))$&Premise \\
$\{2\}$&(2) $\neg S \vee Q$&Premise \\
$\{3\}$&(3) $W \vee \neg T$&Premise \\
$\{4\}$&(4) $\neg W$&Premise \\
$\{1,4\}$&(5) $\neg T \rightarrow (\neg P \vee S)$ & 1 4 T Law of Detachment \\
$\{3,4\}$&(6) $\neg T$ & 3 4 T Modus tollendo ponens\\
$\{1,3,4\}$&(7) $\neg P \vee S$& 5 6 T Law of Detachment \\
$\{2\}$&(8) $S \rightarrow Q$ & 2 T Law of Equivalence of Implication and Disjunction \\
$\{1,3,4\}$&(9) $P \rightarrow S$& 7 T Law of Equivalence of Implication and Disjunction \\
$\{1,2,3,4\}$&(10) $P \rightarrow Q$ & 8 9 T Law of Hypothetical Syllogism \\
$\{1,2,3,4\}$&(11) $\neg P \vee Q$ & 10 T Law of Equivalence of Implication and Disjunction \\
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