��ܸ쵻ˡ No.5

$\displaystyle \forall x P(x)$

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��: $\forall z\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} ((4> z^2) {\Leftrightarrow} (2 >z))$ �� ʤ��ʤ顢Ǥ�դ��ͭ��

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$\displaystyle \exists x P(x)$

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��: $\forall z\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} ((3> z^2) {\Leftrightarrow} (2 >z))$ ��ʤ�� ʤ��

$\displaystyle \exists z\in$ $\displaystyle \mbox{${\mathbb{Q}}$}$ $\displaystyle _{>0} ((3> z^2) \not\Leftrightarrow (2 >z))$

��̤ˡ� $\forall x P(x)$ �� $\exists x (\neg P(x))$ �Ǥ��ꡢ $\exists x P(x)$ �� $\forall x (\neg P(x))$ �Ǥ��롣 ��äơ��㤨��

$\displaystyle \left( \neg(\forall x \exists y \forall z P(x,y,z)) \right) = \left( \exists x \forall y \exists z (\neg P(x,y,z)) \right)$

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$\displaystyle \forall z\in$ $\displaystyle \mbox{${\mathbb{Q}}$}$ $\displaystyle _{>0} ((a> z^2)\ \Leftrightarrow \ (b >z))$

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$\exists y\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} \forall z\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} ((3> z^2) {\Leftrightarrow} (y >z))$
$\forall x\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} \exists y\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} \forall z\in$ $\mbox{${\mathbb{Q}}$}$ $_{>0} ((x> z^2) {\Leftrightarrow} (y >z))$

���ܸ쵻ˡ No.5