Question
~ (p & q) ↔ (~ p v ~ q)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| p | q | ~ p | ~ q | p & q | ~ (p & q) | ~ p v ~ q | ~ (p & q) $\leftrightarrow$ (~ p v ~ q) | |
| 1 | T | T | F | F | T | F | F | T |
| 2 | T | F | F | T | F | T | T | T |
| 3 | F | T | T | F | F | T | T | T |
| 4 | F | F | T | T | F | T | T | T |
| 1 (~) | 2(~) | 1, 2 (&) | 5 (~ ) | 3, 4 (V) | 6, 7 ($\leftrightarrow$) | |||
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| $(R\ S) \rightarrow (F\ E)$ |
| $\sim (R\ S) \rightarrow J$ |
| $(F\ E) \rightarrow \sim H$ |
| $\sim\ \sim H$ |
| $\therefore \sim (J\ v\ G) \& \sim\ \sim H$ |
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $B\ \&\ (A\ v\ D)$ |
| $(A \rightarrow E)\ \&\ (D \rightarrow F)$ |
| $(E\ v\ F) \rightarrow (B\ v\ D)$ |
| $\sim B$ |
| $D$ |
| $(P \leftrightarrow Q) \rightarrow (A \leftrightarrow B)$ |
| $(R \ \&\ S)\ v\ (P \leftrightarrow Q)$ |
| $(F \ \&\ D) \rightarrow \sim\ (R \ \&\ S)$ |
| $(H \ \&\ G)\ v\ (F \ \&\ D)$ |
| $\sim (H \ \&\ G)$ |
| $(A \leftrightarrow B)\ v\ (B \leftrightarrow D)$ |
| $A \rightarrow B$ |
| $C \rightarrow D$ |
| $(\sim\ B\ \&\ P)\ \&\ (A\ v\ C)$ |
| $(D\ v\ Z)\ \&\ \sim B$ |