Question
$A \rightarrow B$
$\sim B$
$\therefore \sim A$
$\sim B$
$\therefore \sim A$
| Support Statement | The resulting statement | ||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | ||
| $A$ | $B$ | $\sim B$ | $A \rightarrow B$ | $(A \rightarrow B)\ \&\ \sim B$ | $\sim A$ | ||
| $1$ | $T$ | $T$ | $F$ | $T$ | $F$ | $F$ | |
| $2$ | $T$ | $F$ | $T$ | $F$ | $F$ | $F$ | |
| $3$ | $F$ | $T$ | $F$ | $T$ | $F$ | $T$ | |
| $4$ | $F$ | $F$ | $T$ | $T$ | $T^*$ | $T^*$ | |
| $2 (\sim )$ | $1, 2 (\rightarrow)$ | $4,3 (\&)$ | $1(\sim )$ | ||||
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| $(A\ v\ D) \rightarrow (R\ \&\ S)$ |
| $E\ v\ (A\ v\ D)$ |
| $F\ \&\ \sim E$ |
| $(R\ \&\ F)\ v\ K$ |
| $A \rightarrow B$ |
| $B \rightarrow S$ |
| $A\ \&\ T$ |
| $\therefore S\ \&\ T$ |
| $(A \rightarrow B) \rightarrow R$ |
| $R \rightarrow S$ |
| $(A \rightarrow B)\ \&\ T$ |
| $S\ \&\ T$ |
| $(X \rightarrow Y)\ v\ D$ |
| $A \rightarrow [(X \rightarrow Y) \rightarrow R]$ |
| $D \rightarrow E$ |
| $(E\ v\ F) \rightarrow A$ |
| $E\ v\ F$ |
| $\therefore (R\ v\ E)\ \&\ A$ |
| $P\ v\ Q$ |
| $R \rightarrow\sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ H$ |