Using the truth table technique outlined above, test the...

Using the truth table technique outlined above, test the following argument forms for validity: $$ \begin{aligned} & \text { 1. } \sim p \vee q \\ & \frac{p}{\therefore \sim q} \end{aligned} $$ $$ \begin{aligned} & \therefore \sim(p \vee q) \\ & \therefore \sim q \end{aligned} $$ $\begin{aligned} & \text { 3. } \sim(p \vee q) \\ & \therefore q \\ & \text { 4. } \sim(p \vee q) \\ & \text { p } \\ & \therefore r \\ & \text { 5. } \sim(p \& q) \\ & \quad \therefore \\ & \therefore \sim p \\ & \text { 6. } \sim(p \& q) \\ & \sim q \\ & \therefore p\end{aligned}$ $$ \begin{aligned} & 7 .(p \& q) \vee(p \& r) \\ & \therefore \overline{p \&(q \vee r)} \\ & 8 .(p \vee q) \&(p \vee r) \\ & \therefore p \&(q \vee r) \\ & \text { 9. } p \& q \\ & \therefore(p \vee r) \&(q \vee r) \\ & \text { 10. } p \vee q \\ & \therefore(p \& r) \vee(q \& r) \end{aligned} $$

Using the truth table technique outlined above, test the following argument forms for validity:
$$
\begin{aligned}
& \text { 1. } \sim p \vee q \\
& \frac{p}{\therefore \sim q}
\end{aligned}
$$
$$
\begin{aligned}
& \therefore \sim(p \vee q) \\
& \therefore \sim q
\end{aligned}
$$
$\begin{aligned} & \text { 3. } \sim(p \vee q) \\ & \therefore q \\ & \text { 4. } \sim(p \vee q) \\ & \text { p } \\ & \therefore r \\ & \text { 5. } \sim(p \& q) \\ & \quad \therefore \\ & \therefore \sim p \\ & \text { 6. } \sim(p \& q) \\ & \sim q \\ & \therefore p\end{aligned}$
$$
\begin{aligned}
& 7 .(p \& q) \vee(p \& r) \\
& \therefore \overline{p \&(q \vee r)} \\
& 8 .(p \vee q) \&(p \vee r) \\
& \therefore p \&(q \vee r) \\
& \text { 9. } p \& q \\
& \therefore(p \vee r) \&(q \vee r) \\
& \text { 10. } p \vee q \\
& \therefore(p \& r) \vee(q \& r)
\end{aligned}
$$

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