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 sav08:logic_and_automata_introduction [2008/05/14 11:05]vkuncak sav08:logic_and_automata_introduction [2015/04/21 17:30] (current) Both sides previous revision Previous revision 2008/05/14 11:06 vkuncak 2008/05/14 11:05 vkuncak 2008/05/14 10:14 vkuncak 2008/05/14 10:13 vkuncak 2008/05/14 10:12 vkuncak 2008/05/14 10:10 vkuncak 2008/05/14 10:05 vkuncak 2008/05/14 10:04 vkuncak 2008/05/14 10:04 vkuncak created Next revision Previous revision 2008/05/14 11:06 vkuncak 2008/05/14 11:05 vkuncak 2008/05/14 10:14 vkuncak 2008/05/14 10:13 vkuncak 2008/05/14 10:12 vkuncak 2008/05/14 10:10 vkuncak 2008/05/14 10:05 vkuncak 2008/05/14 10:04 vkuncak 2008/05/14 10:04 vkuncak created Line 17: Line 17: Compute the unary relation (set) corresponding to this formula $F(z)$: Compute the unary relation (set) corresponding to this formula $F(z)$: - $+ \begin{equation*} ​\exists x. \exists y.\ z = 2 x + 1 \land z = 3 y + 2 ​\exists x. \exists y.\ z = 2 x + 1 \land z = 3 y + 2 -$ + \end{equation*} ++++| ++++| Add 6k to solution, we obtain a solution. \\ Add 6k to solution, we obtain a solution. \\ Line 25: Line 25: Find solutions in set $\{0,​1,​2,​3,​4,​5\}$. \\ Find solutions in set $\{0,​1,​2,​3,​4,​5\}$. \\ - Resulting relation for $F(z)$ is $\{ 6k + 5 \mid k \in \mathbb{Z} \}$. \\ + Resulting relation for $F(z)$ is $\{ 6k + 5 \mid k \in \mathbb{N} \}$. \\ Representation as quantifier-free formula. \\ Representation as quantifier-free formula. \\