Question
(p & ~ q) & (p $\rightarrow$ q)
| 1 | 2 | 3 | 4 | 5 | 6 | |
| p | q | ~ q | p & ~ q | p $\rightarrow$ q | (p & ~ q) & (p $\rightarrow$ q) | |
| 1 | T | T | F | F | T | F |
| 2 | T | F | T | T | F | F |
| 3 | F | T | F | F | T | F |
| 4 | F | F | T | F | T | F |
| 2 (~) | 1, 3 (&) | 1, 2($\rightarrow$) | 4, 5(&) | |||
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| $(J \rightarrow K)\ \&\ R$ |
| $\sim P \rightarrow (A \rightarrow B)$ |
| $P\ v\ (J\ v\ A)$ |
| $\sim P$ |
| $\therefore K\ v\ B$ |
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |
| $R\ \rightarrow\ (A\ \&\ B)$ |
| $P\ v\ \sim\ (S\ \&\ T)$ |
| $\sim\ T\ \&\ \sim\ P$ |
| $(A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ |
| $(\sim\ R\ \&\ \sim\ T)\ v\ D$ |
| $A \rightarrow B$ |
| $C \rightarrow B$ |
| $(\sim\ A\ \&\ \sim \ C)\ \rightarrow\ (D\ \rightarrow\ E)$ |
| $(E\ \rightarrow\ G)\ \&\ (D\ v\ E)$ |
| $E\ v\ G$ |
| $(F \rightarrow S)\ \&\ (R \rightarrow W)$ |
| $F\ \&\ R$ |
| $\therefore \sim S\ \&\ W$ |
| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |