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