Question
$(p \rightarrow q) \rightarrow (\sim p\ v \sim q)$
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | |
| $p$ | $q$ | $\sim p$ | $\sim q$ | $p \rightarrow q$ | $\sim p\ v\ \sim q$ | $(p \rightarrow q) \rightarrow (\sim p\ v\ \sim q)$ | |
| $1$ | $T$ | $T$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $2$ | $T$ | $F$ | $F$ | $T$ | $F$ | $T$ | $T$ |
| $3$ | $F$ | $T$ | $T$ | $F$ | $T$ | $T$ | $T$ |
| $4$ | $F$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $1(\sim )$ | $2(\sim )$ | $1, 2 (\rightarrow)$ | $3, 4 (v)$ | $5, 6 (\rightarrow)$ | |||
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| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $(D \rightarrow Q)\ \&\ ( A\rightarrow B)$ |
| $Q\ \&\ A:$ |
| $\therefore (B\ v\ D)\ \&\ Q$ |
| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |