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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| $(A\ v\ B)\ v\ \sim\ C$ |
| $D\ \rightarrow\ [(A\ v\ B) \rightarrow\ E]$ |
| $F\ \rightarrow (\sim\ C\ \rightarrow\ G)$ |
| $D\ \&\ F$ |
| $(E\ v\ G)\ v\ H$ |
| $(R\ \rightarrow\ S)\ \&\ (A\ v\ C)$ |
| $B\ \&\ (P\ \rightarrow\ W)$ |
| $(W\ \rightarrow\ T)\ \&\ (S\ \rightarrow\ Y)$ |
| $P\ v\ R$ |
| $T\ v\ Y$ |
| $J \rightarrow K$ |
| $J\ v\ (K\ v\ \sim\ L)$ |
| $\sim K$ |
| $\therefore \sim L\ \&\ \sim K$ |