Question
Prove that the following arguments are standard by constructing metaphorical proof
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $(1)\ (A\ v\ B) \rightarrow D$ | $P$ |
| $(2)\ A$ | $P/\therefore (D\ \&\ A)\ v\ P$ |
| $(3)\ A\ v\ B$ | $2,$ Add |
| $(4)\ D$ | $1, 3, MP$ |
| $(5)\ D\ \&\ A$ | $4, 2.$ Conj. |
| $(6)\ (D\ \&\ A)\ v\ P$ | $5,$ Add |
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| $A\ v\ B$ |
| $\sim\ A\ \&\ C$ |
| $\therefore (B\ v\ \sim\ D)\ \&\ C$ |
| $A \rightarrow J$ |
| $B \rightarrow R$ |
| $(A\ v\ B)\&\ \sim D$ |
| $J \rightarrow D$ |
| $\therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |
| $K\rightarrow\ (W\ \rightarrow\ X)$ |
| $( \sim\ Q\ \&\ \sim\ K)\ \rightarrow\ (\sim\ Y\ v\ \sim\ M)$ |
| $(\sim\ Y\ \rightarrow\ \sim\ Z)\ \&\ (\sim\ M\ \rightarrow\ \sim\ P)$ |
| $(W\ \rightarrow\ X)$ |
| $\therefore \sim\ Z\ v\ \sim\ p$ |