Question
$\sim [p\ \&\ r) \rightarrow (p\ v\ q)]$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |
| $(A\ v\ B) \rightarrow (D\ v\ C)$ |
| $(E\ v\ F)\ v\ (A\ v\ B)$ |
| $\sim (A\ v\ B)\ \&\ H$ |
| $F \rightarrow (A\ v\ B)$ |
| $\therefore [E\ \&\ \sim (A\ v\ B)]\ v\ S$ |
| $\sim P\ \&\ (Q\ v\ R)$ |
| $(Q \rightarrow A)\ \&\ (R \rightarrow B)$ |
| $(A\ v\ B) \rightarrow (P\ v\ R)$ |
| $R$ |
| $(A\ \&\ D) \rightarrow C$ |
| $E\rightarrow (B\ v\ D)$ |
| $F \rightarrow (A\ \&\ D)$ |
| $F\ \&\ G$ |
| $C\ v\ (B\ v\ D)$ |
| $P \rightarrow Q$ |
| $\sim Q\ v\ R$ |
| $\sim R$ |
| $\therefore (\sim P \& \sim R)\ v\ S$ |
| $A\ \&\ B.$ |
| $B\rightarrow (D\ v\ E)$ |
| $\sim E$ |
| $D \rightarrow (P \rightarrow \sim Q)$ |
| $\therefore P\rightarrow \sim Q$ |