| $A\ \&\ B.$ |
| $B\rightarrow (D\ v\ E)$ |
| $\sim E$ |
| $D \rightarrow (P \rightarrow \sim Q)$ |
| $\therefore P\rightarrow \sim Q$ |
| $(1)\ A\ \&\ B$ | $P$ |
| $(2)\ B\rightarrow (D\ v\ E)$ | $P$ |
| $(3)\ \sim E$ | $P$ |
| $(4)\ D\rightarrow (P\rightarrow\sim Q)$ | $P/\therefore P\rightarrow\sim Q$ |
| $(5)\ B$ | $1,$ Simp. |
| $(6)\ D\ v\ E$ | $2, 5, MP$ |
| $(7)\ D$ | $6, 3, DS$ |
| $(8)\ P \rightarrow\sim Q$ | $4, 7, MP$ |
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| $N \rightarrow (\sim Z \rightarrow G)$ |
| $D \rightarrow [K\ v\ Y) \rightarrow M]$ |
| $(X\ v\ Y\ v\ \sim\ Z$ |
| $D\ \&\ N$ |
| $\therefore\ (M\ v\ G)\ v\ K$ |
| $(F \rightarrow S)\ \&\ (R \rightarrow W)$ |
| $F\ \&\ R$ |
| $\therefore \sim S\ \&\ W$ |
| $T \rightarrow Q$ |
| $B \rightarrow (K\ v\ T)$ |
| $(N \rightarrow B) \rightarrow (K\ v\ B)$ |
| $K\ v\ (N \rightarrow B)$ |
| $\sim K$ |
| $\therefore\ \sim Q\ v\ Z$ |