Question
$P \rightarrow \sim Q$
$\therefore Q \rightarrow (P\ \&\ Q)$
$\therefore Q \rightarrow (P\ \&\ Q)$
| Support Statement | The resulting statement | ||||||
| $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | ||
| $P$ | $Q$ | $\sim Q$ | $P\ \&\ Q$ | $P\rightarrow\sim Q$ | $Q\rightarrow(P\ \&\ Q)$ | ||
| $1$ | $T$ | $T$ | $F$ | $T$ | $F$ | $T$ | |
| $2$ | $T$ | $F$ | $T$ | $F$ | $T$ | $T$ | |
| $3$ | $F$ | $T$ | $F$ | $F$ | $T^*$ | $F^*$ | |
| $4$ | $F$ | $F$ | $T$ | $F$ | $T$ | $T$ | |
| $2 (\sim )$ | $1, 2(\&)$ | $1, 3 (\rightarrow)$ | $2, 4 (\rightarrow)$ | ||||
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| $(A\ \&\ B) \rightarrow\ \sim\ R$ |
| $R\ v\ \sim \ D$ |
| $T \rightarrow B$ |
| $D\ v\ (B \rightarrow P)$ |
| $A\ \&\ B$ |
| $\therefore (T\ P)\ v\ L$ |
| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |
| $B\ \&\ (A\ v\ D)$ |
| $(A \rightarrow E)\ \&\ (D \rightarrow F)$ |
| $(E\ v\ F) \rightarrow (B\ v\ D)$ |
| $\sim B$ |
| $D$ |