| $(P \rightarrow Q)\ \&\ (R \rightarrow S)$ |
| $(Q \rightarrow T)\ \&\ (S \rightarrow P)$ |
| $\sim T$ |
| $\therefore \sim R\ \&\ \sim T$ |
| $(1)\ (P \rightarrow Q)\ \&\ (R \rightarrow S)$ | $P$ |
| $(2)\ (Q \rightarrow T)\ \&\ (S \rightarrow P)$ | $P$ |
| $(3)\ \sim 7$ | $P/ \therefore \sim R\ \&\ \sim T$ |
| $(4)\ Q \rightarrow T$ | $2,$ Simp. |
| $(5)\ \sim Q$ | $4, 3, MT$ |
| $(6)\ P \rightarrow Q$ | $1,$ Simp. |
| $(7)\ \sim P$ | $6, 5, MT$ |
| $(8)\ S \rightarrow P$ | $1,$ Simp. |
| $(9)\ \sim S$ | $8, 7, MT$ |
| $(10)\ R \rightarrow S$ | $1,$ Simp. |
| $(11)\ \sim R$ | $10, 9, MT$ |
| $(12)\ \sim R\ \&\ \sim T$ | $11, 3,$ Conj. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(A\ v\ B)\ \rightarrow\ [D\ \rightarrow\ (P\ \&\ \sim\ Q)]$ |
| $(A\ \&\ J)\ \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore\ (D \rightarrow\ K)\ v\ \sim\ Q$ |
| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| $(K \rightarrow P) \rightarrow B$ |
| $\sim R$ |
| $(K \rightarrow P)\ v\ B$ |
| $B \rightarrow R$ |
| $\therefore\ \sim (K \rightarrow P)\ \&\ B$ |