Question
A$\rightarrow$ ~ B
B
$\therefore$ ~ A
B
$\therefore$ ~ A
| Support Statement | The resulting statement | ||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| A | B | ~ A | ~ B | A$\rightarrow$ ~ B | (A$\rightarrow$ ~ B) & B | ~ A | |
| 1 | T | T | F | F | F | F | F |
| 2 | T | F | F | T | T | F | F |
| 3 | F | T | T | F | T | T$^*$ | T$^*$ |
| 4 | F | F | T | T | T | F | T |
| 1(~) | 2(~) | 1, 4($\rightarrow$) | 5, 2(&) | As 3 | |||
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| $(P \leftrightarrow Q) \rightarrow (A \leftrightarrow B)$ |
| $(R \ \&\ S)\ v\ (P \leftrightarrow Q)$ |
| $(F \ \&\ D) \rightarrow \sim\ (R \ \&\ S)$ |
| $(H \ \&\ G)\ v\ (F \ \&\ D)$ |
| $\sim (H \ \&\ G)$ |
| $(A \leftrightarrow B)\ v\ (B \leftrightarrow D)$ |
| $(P\ \&\ Q) \rightarrow R$ |
| $R \rightarrow (H \rightarrow G)$ |
| $H\ \&\ K$ |
| $P\ \&\ Q$ |
| $\therefore (G\ v\ I)\ \&\ H$ |
| (P$\rightarrow$Q) & (R v S) |
| (R v S) $\rightarrow$ ~ L |
| L v (M & N) |
| $\therefore$ [(P $\rightarrow$ Q) & M] & ~ L |
| $A\ v\ B$ |
| $\sim\ A\ \&\ C$ |
| $\therefore (B\ v\ \sim\ D)\ \&\ C$ |
| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |