Question
(p → q) ↔ (~ p v q)
| 1 | 2 | 3 | 4 | 5 | 6 | |
| p | q | ~ p | p $\rightarrow$ q | ~ p v q | (p $\rightarrow$ q)$\rightarrow$ (~ p v q) | |
| 1 | T | T | F | T | T | T |
| 2 | T | F | F | F | F | T |
| 3 | F | T | T | T | T | T |
| 4 | F | F | T | T | T | T |
| 1 (~) | 1, 2 ($\rightarrow$) | 3, 2 (v) | 4, 5 ($\leftrightarrow$) | |||
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| $\sim\ L\ \rightarrow\ \sim\ N$ |
| $(A\ v\ B)\ \rightarrow\ Q$ |
| $Q\ \rightarrow\ [(S\ \&\ T) \rightarrow\ P]$ |
| $(S\ \&\ T)\ v\ \sim\ L$ |
| $A\ v\ B$ |
| $\therefore\ (P\ v\ \sim\ N)\ \&\ Q$ |
| $N \rightarrow (\sim Z \rightarrow G)$ |
| $D \rightarrow [K\ v\ Y) \rightarrow M]$ |
| $(X\ v\ Y\ v\ \sim\ Z$ |
| $D\ \&\ N$ |
| $\therefore\ (M\ v\ G)\ v\ K$ |
| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |
| $A \rightarrow B$ |
| $C \rightarrow B$ |
| $(\sim\ A\ \&\ \sim \ C)\ \rightarrow\ (D\ \rightarrow\ E)$ |
| $(E\ \rightarrow\ G)\ \&\ (D\ v\ E)$ |
| $E\ v\ G$ |
| $(A\ v\ B) \rightarrow (D\ v\ C)$ |
| $(E\ v\ F)\ v\ (A\ v\ B)$ |
| $\sim (A\ v\ B)\ \&\ H$ |
| $F \rightarrow (A\ v\ B)$ |
| $\therefore [E\ \&\ \sim (A\ v\ B)]\ v\ S$ |