Question
Determine the validity of the following arguments using the direct method of truth table
$P\ v\ Q$
$\sim P$
$\therefore Q$
$P\ v\ Q$
$\sim P$
$\therefore Q$
| Support Statement | The resulting statement | ||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | ||
| $P$ | $Q$ | $\sim P$ | $P\ v\ Q$ | $(P\ v\ Q)\ \&\ \sim P$ | $Q$ | ||
| $1$ | $T$ | $T$ | $F$ | $T$ | $F$ | $T$ | |
| $2$ | $T$ | $F$ | $F$ | $T$ | $F$ | $F$ | |
| $3$ | $F$ | $T$ | $T$ | $T$ | $T^*$ | $T^*$ | |
| $4$ | $F$ | $F$ | $T$ | $F$ | F | $F$ | |
| $1 (\sim )$ | $1, 2(v)$ | $4, 3(\&)$ | As $2$ | ||||
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $R \rightarrow S$ |
| $P \rightarrow Q$ |
| $P\ v\ Q$ |
| $Q \rightarrow R$ |
| $\therefore (P \rightarrow R) \& (R\ v\ S)$ |
| $M\ \rightarrow\ N$ |
| $D\ v\ (N\ \rightarrow\ P)$ |
| $R\ v\ \sim\ D$ |
| $(A\ \&\ B)\ \rightarrow\ \sim\ R$ |
| $A\ \&\ B$ |
| $(M \rightarrow P)\ v\ Z$ |
| $(P \rightarrow\ Q)\ \&\ R$ |
| $E\ \&\ F$ |
| $\therefore [(F\ \&\ G)\ \&\ R ]\ \&\ E$ |