Question
(p $\rightarrow$ q) $\leftrightarrow$ (~ p $\rightarrow$ ~ q)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| p | q | p $\rightarrow$ q | ~ p | ~ q | ~ p $\rightarrow$ ~ q | (p $\rightarrow$ q) $\leftrightarrow$ (~ p $\rightarrow$ ~ q) | |
| 1 | T | T | T | F | F | T | T |
| 2 | T | F | F | F | T | T | F |
| 3 | F | T | T | T | F | F | F |
| 4 | F | F | T | T | T | T | T |
| 1, 2 ($\rightarrow$) | 1 (~) | 2 (~) | 4, 5($\rightarrow$) | 3, 6 ($\leftrightarrow$) | |||
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| $(A\ \&\ D) \rightarrow C$ |
| $E\rightarrow (B\ v\ D)$ |
| $F \rightarrow (A\ \&\ D)$ |
| $F\ \&\ G$ |
| $C\ v\ (B\ v\ D)$ |
| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |
| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $A\ \&\ B.$ |
| $B\rightarrow (D\ v\ E)$ |
| $\sim E$ |
| $D \rightarrow (P \rightarrow \sim Q)$ |
| $\therefore P\rightarrow \sim Q$ |
| $A \rightarrow B$ |
| $C \rightarrow B$ |
| $(\sim\ A\ \&\ \sim \ C)\ \rightarrow\ (D\ \rightarrow\ E)$ |
| $(E\ \rightarrow\ G)\ \&\ (D\ v\ E)$ |
| $E\ v\ G$ |