Question
$(p\ V\ \sim\ \sim p)$
| $1$ | $2$ | $3$ | $4$ | $5$ | |
| $p$ | $\sim p$ | $\sim\ \sim\ p$ | $p\ v \sim\ \sim\ p$ | $\sim (p\ v\ \sim\ \sim p)$ | |
| $1$ | $T$ | $F$ | $T$ | $T$ | $F$ |
| $2$ | $F$ | $T$ | $F$ | $F$ | $T$ |
| $1(\sim )$ | $2 (\sim )$ | $1, 3 (V)$ | $4(\sim )$ | ||
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| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |
| $(W\ O\ \rightarrow\ T)\ \&\ (F\ \rightarrow\ Y)$ |
| $B\ \&\ (P\ \rightarrow\ W)$ |
| $(E\ \rightarrow\ F)\ \&\ (H\ v\ I)$ |
| $P\ v\ E$ |
| $\therefore\ B\ \&\ (T\ v\ Y)$ |
| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |
| $(X \rightarrow Y)\ v\ D$ |
| $A \rightarrow [(X \rightarrow Y) \rightarrow R]$ |
| $D \rightarrow E$ |
| $(E\ v\ F) \rightarrow A$ |
| $E\ v\ F$ |
| $\therefore (R\ v\ E)\ \&\ A$ |