| $R\ \rightarrow\ (A\ \&\ B)$ |
| $P\ v\ \sim\ (S\ \&\ T)$ |
| $\sim\ T\ \&\ \sim\ P$ |
| $(A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ |
| $(\sim\ R\ \&\ \sim\ T)\ v\ D$ |
| $(1)\ R\ \rightarrow\ (A\ \&\ B )$ | $P$ |
| $(2)\ P\ v\ \sim\ (S\ \&\ T)$ | $P$ |
| $(3)\ \sim\ T\ \&\ \sim\ P$ | $P$ |
| $(4)\ (A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ | $P/\ (\sim\ R\ \&\ \sim \ T)\ v\ D$ |
| $(5)\ \sim\ P$ | $3,$ Simp. |
| $(6)\ \sim\ (S\ \&\ T)$ | $2, 5, DS$ |
| $(7)\ \sim\ (A\ \&\ B)$ | $4, 6, MT$ |
| $(8)\ \sim\ R$ | $1, 7, MT$ |
| $(9)\ \sim\ T$ | $3,$ Simp. |
| $(10)\ \sim\ R\ \&\ \sim\ T$ | $8, 9,$ Conj. |
| $(11)\ (\sim\ R\ \&\ \sim\ T)\ v\ D$ | $10,$ Add. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $M\ \rightarrow\ N$ |
| $D\ v\ (N\ \rightarrow\ P)$ |
| $R\ v\ \sim\ D$ |
| $(A\ \&\ B)\ \rightarrow\ \sim\ R$ |
| $A\ \&\ B$ |
| $(M \rightarrow P)\ v\ Z$ |
| $(A\ \&\ B) \rightarrow\ \sim\ R$ |
| $R\ v\ \sim \ D$ |
| $T \rightarrow B$ |
| $D\ v\ (B \rightarrow P)$ |
| $A\ \&\ B$ |
| $\therefore (T\ P)\ v\ L$ |
| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $G \rightarrow J$ |
| $J \rightarrow K$ |
| $(G \rightarrow K) v (J \rightarrow L)$ |
| $L \rightarrow M$ |
| $\therefore (J \rightarrow M) v\ Q$ |
| $H \rightarrow (I \rightarrow J)$ |
| $K \rightarrow (I \rightarrow J)$ |
| $(\sim H\ \&\ \sim K) \rightarrow (\sim\ L\ v\ \sim M)$ |
| $(\sim L \rightarrow\ \sim N)\ \&\ (\sim M \rightarrow \sim Q)$ |
| $\sim (I \rightarrow J)$ |
| $\sim N\ v\ \sim Q$ |