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