| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $(1)\ M\rightarrow \sim (S \ \&\ T)$ | $P$ |
| $(2)\ \sim (A \ \&\ B)\ v\sim D$ | $P$ |
| $(3)\ \sim D \rightarrow (S \ \&\ T)$ | $P$ |
| $(4)\ M$ | $P/[\sim (A \ \&\ B)\ \ \&\ M]\ v\ D$ |
| $(5)\ \sim (S \ \&\ T)$ | $1, 4, MP$ |
| $(6)\ \sim\ \sim D$ | $3, 5, MT$ |
| $(7)\ \sim (A \ \&\ B)$ | $2, 6, DS$ |
| $(8)\ \sim (A \ \&\ B)\ \ \&\ M$ | $7, 4,$ Conj. |
| $(9)\ [\sim (A \ \&\ B)\ \ \&\ M]\ v\ D$ | $8,$ Add. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(A\ v\ B)\ \rightarrow [D\ \rightarrow\ (P\ \&\ \sim \ Q)]$ |
| $(A\ \&\ J) \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore (D\rightarrow K)\ v\ \sim\ Q$ |
| $(P\ v\ R)\ \rightarrow (S\ v\ T)$ |
| $\sim M\ \&\ \sim N$ |
| $N\ v \sim (S\ v\ T)$ |
| $H \rightarrow (P\ v\ R)$ |
| $[\sim H\ \&\ \sim (P\ v\ R)]\ v\ S$ |