Question
$(p \rightarrow q)\ \&\ \sim (p \rightarrow q)$
| $1$ | $2$ | $3$ | $4$ | $5$ | |
| $p$ | $q$ | $p \rightarrow q$ | $\sim (p \rightarrow q)$ | $(p \rightarrow q)\ \&\ \sim\ (p \rightarrow q)$ | |
| $1$ | $T$ | $T$ | $T$ | $F$ | $F$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $F$ |
| $3$ | $F$ | $T$ | $T$ | $F$ | $F$ |
| $4$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $1, 2 ( \rightarrow )$ | $3(\sim )$ | $3, 4 (\&)$ | |||
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| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| $H \rightarrow I$ |
| $H\ \&\ J$ |
| $I \rightarrow G$ |
| $G\ \&\ J$ |