Question
~ Q v R
| Column $\rightarrow$ | 1 | 2 | 3 | 4 |
| Row $\downarrow$ | Q | P | ~ Q | ~ Q v P |
| 1 | T | T | F | T |
| 2 | T | F | F | F |
| 3 | F | T | T | T |
| 4 | F | F | T | T |
| 1(~) | 3, 2 (v) | |||
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| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| (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 |
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |
| $M\ \rightarrow\ N$ |
| $D\ v\ (N\ \rightarrow\ P)$ |
| $R\ v\ \sim\ D$ |
| $(A\ \&\ B)\ \rightarrow\ \sim\ R$ |
| $A\ \&\ B$ |
| $(M \rightarrow P)\ v\ Z$ |