| $\sim (A \ \&\ B) \rightarrow H$ |
| $F\ v \sim (H \ \&\ F)$ |
| $(A \ \&\ B) \rightarrow (H \ \&\ F)$ |
| $\sim F \ \&\ (D \ \&\ E)$ |
| $(D \ \&\ E) \ \&\ H$ |
| $(1)\ \sim (A \ \&\ B)\ \rightarrow H$ | $P$ |
| $(2)\ F\ v \sim (H \ \&\ F)$ | $P$ |
| $(3)\ (A \ \&\ B)\ \rightarrow (H \ \&\ F)$ | $P$ |
| $(4)\ \sim F \ \&\ (D \ \&\ E)$ | $P/ (D \ \&\ E)\ \&\ H$ |
| $(5)\ \sim F$ | $4,$ Simp. |
| $(6)\ \sim (H \ \&\ F)$ | $2, 5, DS$ |
| $(7)\ \sim (A \ \&\ B)$ | $3, 6, MT$ |
| $(8)\ H$ | $1, 7, MP$ |
| $(9)\ D \ \&\ E$ | $4,$ Simp. |
| $(10)\ (D \ \&\ E)\ \&\ H$ | $9, 8,$ Conj. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $P \rightarrow Q$ |
| $\sim Q\ v\ R$ |
| $\sim R$ |
| $\therefore (\sim P \& \sim R)\ v\ S$ |
| $(K \rightarrow P) \rightarrow B$ |
| $\sim R$ |
| $(K \rightarrow P)\ v\ B$ |
| $B \rightarrow R$ |
| $\therefore\ \sim (K \rightarrow P)\ \&\ B$ |
| $(E\rightarrow F)\rightarrow H$ |
| $\sim J\ v (F\ \&\ G)$ |
| $F \rightarrow(H\rightarrow I)$ |
| $\sim\ \sim J$ |
| $G\ \&\ [(E\rightarrow F) \rightarrow I]$ |
| $H \rightarrow (I \rightarrow J)$ |
| $K \rightarrow (I \rightarrow J)$ |
| $(\sim H\ \&\ \sim K) \rightarrow (\sim\ L\ v\ \sim M)$ |
| $(\sim L \rightarrow\ \sim N)\ \&\ (\sim M \rightarrow \sim Q)$ |
| $\sim (I \rightarrow J)$ |
| $\sim N\ v\ \sim Q$ |
| $(R\ \&\ S)\ v\ P$ |
| $P\ \rightarrow\ Q$ |
| $T\ v\ (R\ \&\ S)\ \rightarrow\ W ]$ |
| $S\ \&\ \sim\ T$ |
| $[S\ \&\ (W\ v\ Q)]\ v\ \sim\ P$ |