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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| (~ 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 |
| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |