Answer
See steps below.
Work Step by Step
Use Valid Argument Forms in Table 2.3.1, we have:
1. $u\vee w$ $\ \ \ \ \ $by e.
$\ \ \ \ \ \sim w$ $\ \ \ \ \ $by d.
$\ \ \therefore\ u \ \ \ \ \ \ \ \ \ $by Elimination.
2. $u\rightarrow (\sim p)$ $\ \ \ \ \ $by c.
$\ \ \ \ u$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $by 1.
$\ \ \therefore\ \sim p$ $ \ \ \ \ \ \ \ \ \ \ \ $by Modus Ponens.
3. $(\sim p)\rightarrow (r\wedge\sim s)$ $\ \ \ \ \ $by a.
$\ \ \ \ \ \sim p$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $by 2.
$\ \ \therefore \ r\wedge\sim s \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $by Modus Ponens.
4. $r\wedge(\sim s)$ $\ \ \ \ \ $by 3.
$\ \ \therefore \ \sim s \ \ \ \ \ \ \ \ \ \ $by Specialization.
5. $t\rightarrow s$ $\ \ \ \ \ $by b.
$\ \ \ \ \ \sim s$ $\ \ \ \ \ \ $by 4.
$\ \therefore \ \sim t \ \ \ \ \ \ $by Modus Tollens.
