Question
$\sim P \rightarrow\ \sim Q$
$\sim Q$
$\therefore \sim P$
$\sim Q$
$\therefore \sim P$
| Support Statement | The resulting statement | ||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | |
| $P$ | $Q$ | $\sim P$ | $\sim Q$ | $\sim P \rightarrow \sim Q$ | $(\sim P \rightarrow \sim Q)\ \&\ \sim Q$ | $\sim P$ | |
| $1$ | $T$ | $T$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $T$ | $T^*$ | $F^*$ |
| $3$ | $F$ | $T$ | $T$ | $F$ | $F$ | $F$ | $T$ |
| $4$ | $F$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $1(\sim )$ | $2(\sim )$ | $3, 4(\rightarrow)$ | $5, 4 (\&)$ | As $3$ | |||
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| $H \rightarrow ( I\ \&\ \sim J)$ |
| $( I\ v\ G) \rightarrow K$ |
| $H$ |
| $\sim K\ \&\ I$ |
| $(A\ \rightarrow\ B)\ \&\ (D\ \rightarrow\ E)$ |
| $(B\ \rightarrow\ T)\ \&\ (E\ \rightarrow\ A)$ |
| $\sim\ T$ |
| $\therefore\ \sim\ D\ \&\ \sim\ T$ |
| $R\ \rightarrow\ (S\ v\ T)$ |
| $P\ v((S\ v\ T)\ \rightarrow\ W]$ |
| $M\ v\ \sim\ P$ |
| $(H\ \&\ N)\ \rightarrow\ \sim\ M$ |
| $H\ \&\ N$ |
| $(R\ \rightarrow\ W)\ v\ S$ |