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