Question
(p & q) & (~ q $\rightarrow$ ~p)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| p | q | ~ p | ~ q | p & q | ~ q $\rightarrow$~ p) | (p & q) & (~ q $\rightarrow$ ~p) | |
| 1 | T | T | F | F | T | T | T |
| 2 | T | F | F | T | F | F | F |
| 3 | F | T | T | F | F | T | F |
| 4 | F | F | T | T | F | T | F |
| 1 (~) | 2(~) | 2, 4 (&) | 3, 5 (V) | 1, 6 ($\leftrightarrow$) | |||
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| $(A\ v\ B)\ \rightarrow\ [D\ \rightarrow\ (P\ \&\ \sim\ Q)]$ |
| $(A\ \&\ J)\ \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore\ (D \rightarrow\ K)\ v\ \sim\ Q$ |
| $P \rightarrow Q$ |
| $P\ \&\ \sim S$ |
| $\therefore Q\ \&\ \sim P$ |
| $(A\ \rightarrow\ B)\ v\ D$ |
| $H\ \rightarrow\ [(A \ \rightarrow\ B)\ \rightarrow\ R]$ |
| $D\ \rightarrow\ E$ |
| $(E\ v\ F)\ \rightarrow\ H$ |
| $E\ v\ F$ |
| $(R\ v\ E)\ \&\ H$ |
| $H \rightarrow ( I\ \&\ \sim J)$ |
| $( I\ v\ G) \rightarrow K$ |
| $H$ |
| $\sim K\ \&\ I$ |
| $K\rightarrow\ (W\ \rightarrow\ X)$ |
| $( \sim\ Q\ \&\ \sim\ K)\ \rightarrow\ (\sim\ Y\ v\ \sim\ M)$ |
| $(\sim\ Y\ \rightarrow\ \sim\ Z)\ \&\ (\sim\ M\ \rightarrow\ \sim\ P)$ |
| $(W\ \rightarrow\ X)$ |
| $\therefore \sim\ Z\ v\ \sim\ p$ |