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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| $P \rightarrow Q$ |
| $\sim Q\ v\ R$ |
| $\sim R$ |
| $\therefore (\sim P \& \sim R)\ v\ S$ |
| $(X \rightarrow Y)\ v\ D$ |
| $A \rightarrow [(X \rightarrow Y) \rightarrow R]$ |
| $D \rightarrow E$ |
| $(E\ v\ F) \rightarrow A$ |
| $E\ v\ F$ |
| $\therefore (R\ v\ E)\ \&\ A$ |