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