Question
$P\ v (Q\ \&\ R)$
$\sim P$
$\therefore Q\ \&\ R$
$\sim P$
$\therefore Q\ \&\ R$
| Support Statement | The resulting statement | |||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | |
| $P$ | $Q$ | $R$ | $\sim P$ | $Q\ \&\ R$ | $P\ v\ (Q\ \&\ R)$ | $[P\ v\ (Q\ \&\ R)]\ \& \sim P$ | $Q\ \&\ R$ | |
| $1$ | $T$ | $T$ | $T$ | $F$ | $T$ | $T$ | $F$ | $T$ |
| $2$ | $T$ | $T$ | $F$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $3$ | $T$ | $F$ | $T$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $4$ | $T$ | $F$ | $F$ | $F$ | $F$ | $T$ | $F$ | $F$ |
| $5$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T^*$ | $T^*$ |
| $6$ | $F$ | $T$ | $F$ | $T$ | $F$ | $F$ | $F$ | $F$ |
| $7$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $F$ | $F$ |
| $8$ | $F$ | $F$ | $F$ | $T$ | $F$ | $F$ | $F$ | $F$ |
| $1 (\sim )$ | $2,3 (\&)$ | $1, 5 (v)$ | $6, 4 (\&)$ | As $5$ | ||||
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $\sim (A \ \&\ B) \rightarrow H$ |
| $F\ v \sim (H \ \&\ F)$ |
| $(A \ \&\ B) \rightarrow (H \ \&\ F)$ |
| $\sim F \ \&\ (D \ \&\ E)$ |
| $(D \ \&\ E) \ \&\ H$ |
| $T \rightarrow B$ |
| $B \rightarrow ( \sim\ P \rightarrow\ \sim\ Q)$ |
| $\sim\ P\ \&\ \sim\ R$ |
| $T$ |
| $\therefore\sim\ Q\ v\ X$ |
| $P \rightarrow Q$ |
| $P\ \&\ \sim S$ |
| $\therefore Q\ \&\ \sim P$ |
| $(K \rightarrow P) \rightarrow B$ |
| $\sim R$ |
| $(K \rightarrow P)\ v\ B$ |
| $B \rightarrow R$ |
| $\therefore\ \sim (K \rightarrow P)\ \&\ B$ |