Question
~ P → ~ Q
| Column $\rightarrow$ | 1 | 2 | 3 | 4 | 5 |
| Row $\downarrow$ | P | Q | ~P | ~ Q | ~P $\rightarrow$ ~ Q |
| 1 | T | T | F | F | T |
| 2 | T | F | F | T | T |
| 3 | F | T | T | F | F |
| 4 | F | F | T | T | T |
| 1(~) | 2 (~) | 3, 4 ($\rightarrow$) | |||
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| $(A\ v\ B)\ \rightarrow [D\ \rightarrow\ (P\ \&\ \sim \ Q)]$ |
| $(A\ \&\ J) \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore (D\rightarrow K)\ v\ \sim\ Q$ |
| $J \rightarrow K$ |
| $J\ v\ (K\ v\ \sim\ L)$ |
| $\sim K$ |
| $\therefore \sim L\ \&\ \sim K$ |
| $P \rightarrow (Q\ v\ R)$ |
| $P \rightarrow S$ |
| $P\ v\ T$ |
| $\sim T$ |
| $\therefore S\ \&\ (Q\ v\ R)$ |
| $R \rightarrow S$ |
| $P \rightarrow Q$ |
| $P\ v\ Q$ |
| $Q \rightarrow R$ |
| $\therefore (P \rightarrow R) \& (R\ v\ S)$ |
| $(T\ \&\ P) \rightarrow \sim Q$ |
| $\sim (T\ \&\ P) \rightarrow (R \rightarrow \sim Q)$ |
| $(\sim S\ v\ R)\rightarrow\ \sim\ \sim Q$ |
| $\sim S$ |
| $\therefore \sim R\ \&\ \sim S$ |