Question
$\sim p \rightarrow (p\ v\ q)$
| $1$ | $2$ | $3$ | $4$ | $5$ | |
| $p$ | $q$ | $\sim p$ | $p\ v\ q$ | $\sim p \rightarrow (p\ v\ q)$ | |
| $1$ | $T$ | $T$ | $F$ | $T$ | $T$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $T$ |
| $3$ | $F$ | $T$ | $T$ | $T$ | $T$ |
| $4$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $1 (\sim )$ | $1, 2 (V)$ | $3, 4 (\rightarrow)$ | |||
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| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| $N \rightarrow (\sim Z \rightarrow G)$ |
| $D \rightarrow [K\ v\ Y) \rightarrow M]$ |
| $(X\ v\ Y\ v\ \sim\ Z$ |
| $D\ \&\ N$ |
| $\therefore\ (M\ v\ G)\ v\ K$ |
| (G $\rightarrow$ H) $\rightarrow$ (I $\leftrightarrow$ J) |
| K v ~(L $\rightarrow$ M) |
| (G $\rightarrow$ H) v ~ K |
| N $\rightarrow$ (L $\rightarrow$ M) |
| ~ (I J) |
| $\therefore$~ N & ~ K |
| $(P\ \&\ R)\ v\ (S\ \rightarrow\ T)$ |
| $Q \rightarrow \sim\ (P\ \&\ R)$ |
| $P\ v\ Q$ |
| $\sim\ P$ |
| $(S\ \rightarrow\ T)\ \&\ Q$ |
| $E\ v\ (E\ \&\ Q)$ |
| $E \rightarrow L$ |
| $\sim L$ |
| $Q\ v\ M$ |
| $(A\ v\ B)\ \rightarrow\ D$ |
| $E\ \rightarrow\ \sim\ D$ |
| $(G\ \leftrightarrow\ F)\ \rightarrow\ (E\ \&\ H)$ |
| $G\ \leftrightarrow\ F$ |
| $\sim\ (A\ v\ B)\ \&\ H$ |