Question
$p \rightarrow [q\ \&\ (p \rightarrow r)]$
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | |
| $p$ | $q$ | $r$ | $p \rightarrow r$ | $q\ \&\ (p \rightarrow r)$ | $p \rightarrow [q\ \&\ (p \rightarrow r)]$ | |
| $1$ | $T$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $2$ | $T$ | $T$ | $F$ | $F$ | $F$ | $F$ |
| $3$ | $T$ | $F$ | $T$ | $T$ | $F$ | $F$ |
| $4$ | $T$ | $F$ | $F$ | $F$ | $F$ | $F$ |
| $5$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $6$ | $F$ | $T$ | $F$ | $T$ | $T$ | $T$ |
| $7$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
| $8$ | $F$ | $F$ | $F$ | $T$ | $F$ | $T$ |
| $1, 3 (\rightarrow)$ | $2, 4 (\&)$ | $1, 5 (\rightarrow)$ | ||||
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(P\ v\ Q)\ \rightarrow\ (T\ v\ S)$ |
| $\sim\ N\ \& \sim\ M$ |
| $N\ v\ \sim\ (T\ v\ S)$ |
| $H\ \rightarrow\ (P\ v\ Q)$ |
| $\therefore \sim\ H\ \&\ \sim\ M$ |
| $(P\ \&\ R)\ v\ \sim\ S$ |
| $(P\ \&\ R)\ \rightarrow\ \sim\ T$ |
| $M\ \rightarrow\ \sim\ \sim\ T$ |
| $M$ |
| $M\ \&\ \sim\ S$ |
| $P \rightarrow (Q\ v\ R)$ |
| $P \rightarrow S$ |
| $P\ v\ T$ |
| $\sim T$ |
| $\therefore S\ \&\ (Q\ v\ R)$ |
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |