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