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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| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| (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 |
| $(A\ \&\ B)\ \rightarrow\ P$ |
| $\sim\ P\ \&\ \sim\ Q$ |
| $(J\ \rightarrow\ K)\ \rightarrow\ Q$ |
| $\sim\ (A\ \&\ B)\ \&\ \sim\ (J\ \rightarrow\ K)$ |