Question
$\sim p (p\ v\ \sim q)\ \&\ \sim (q\ v\ \sim p)$
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | |
| $p$ | $q$ | $\sim p$ | $\sim q$ | $p v \sim q$ | $q v \sim p$ | $\sim (p v \sim q)$ | $\sim (q v \sim p)$ | $\sim\ p\ (p\ v\ \sim q)\ \&\ \sim (q\ v\ \sim\ p)$ | |
| $1$ | $T$ | $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $F$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $T$ | $F$ |
| $3$ | $F$ | $T$ | $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ |
| $4$ | $F$ | $F$ | $T$ | $T$ | $T$ | $T$ | $F$ | $F$ | $F$ |
| $1 (\sim )$ | $2(\sim )$ | $1, 4(V)$ | $2, 3(V)$ | $5(\sim )$ | $6(\sim )$ | $7, 8(\&)$ | |||
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| $R\ \rightarrow\ (S\ v\ T)$ |
| $P\ v((S\ v\ T)\ \rightarrow\ W]$ |
| $M\ v\ \sim\ P$ |
| $(H\ \&\ N)\ \rightarrow\ \sim\ M$ |
| $H\ \&\ N$ |
| $(R\ \rightarrow\ W)\ v\ S$ |
| $R \rightarrow S$ |
| $P \rightarrow Q$ |
| $P\ v\ Q$ |
| $Q \rightarrow R$ |
| $\therefore (P \rightarrow R) \& (R\ v\ S)$ |
| $H \rightarrow ( I\ \&\ \sim J)$ |
| $( I\ v\ G) \rightarrow K$ |
| $H$ |
| $\sim K\ \&\ I$ |
| $\sim P\ \&\ (Q\ v\ R)$ |
| $(Q \rightarrow A)\ \&\ (R \rightarrow B)$ |
| $(A\ v\ B) \rightarrow (P\ v\ R)$ |
| $R$ |
| $G \rightarrow J$ |
| $J \rightarrow K$ |
| $(G \rightarrow K) v (J \rightarrow L)$ |
| $L \rightarrow M$ |
| $\therefore (J \rightarrow M) v\ Q$ |