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