Question
(A → B) (~ A v ~ B)
| Column $\rightarrow$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Row $\downarrow$ | A | B | ~A | ~ B | A$\rightarrow$B | ~ A v ~ B | (A$\rightarrow$B) $\rightarrow$ (~ A v ~ B) |
| 1 | T | T | F | F | T | F | F |
| 2 | T | F | F | T | F | T | T |
| 3 | F | T | T | F | T | T | T |
| 4 | F | F | T | T | T | T | T |
| 1(~) | 2(~) | 1, 2 ($\rightarrow$) | 3, 4 (v) | 5, 6 ($\rightarrow$) |
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| $(M\ v\ N)\ \&\ K$ |
| $[M\ v\ N)\ v\ L] \rightarrow H$ |
| $[( M\ v\ N)\ \&\ H] \rightarrow Z$ |
| $\therefore Z$ |
| $(A\ \&\ B)\ \rightarrow\ P$ |
| $\sim\ P\ \&\ \sim\ Q$ |
| $(J\ \rightarrow\ K)\ \rightarrow\ Q$ |
| $\sim\ (A\ \&\ B)\ \&\ \sim\ (J\ \rightarrow\ K)$ |
| $P \rightarrow Q$ |
| $P\ \&\ \sim S$ |
| $\therefore Q\ \&\ \sim P$ |
| $(J \rightarrow K)\ \&\ R$ |
| $\sim P \rightarrow (A \rightarrow B)$ |
| $P\ v\ (J\ v\ A)$ |
| $\sim P$ |
| $\therefore K\ v\ B$ |
| $(M \leftrightarrow N) \rightarrow O$ |
| $\sim A\ v\ (B\ \&\ D)$ |
| $B \rightarrow (O \rightarrow P)$ |
| $\sim \sim A$ |
| $\therefore (M \leftrightarrow N) \rightarrow P$ |
| $(P \rightarrow\ Q)\ \&\ R$ |
| $E\ \&\ F$ |
| $\therefore [(F\ \&\ G)\ \&\ R ]\ \&\ E$ |