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\(1.\ S\rightarrow T \)
\(2.\ \sim T \)
\(3.\ (\sim S\vee U)\rightarrow R \)
\(4.\ R\rightarrow (P\cdot \sim Q)\) \( / \therefore P\vee Q\)
\(5.\ \sim S\) 1, 2 Modus Tollens
\(6.\ \sim S \vee U\) 5 Addition
\(7.\ R\) 3, 6 Modus Ponens
\(8.\ P \cdot \sim Q\) 4, 7 Modus Ponens
\(9.\ P\) 8 Simp.
\(10.\ P\vee Q\) 9 Add.