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