[Logica] Forma prenex

[perplesso1]

Devo ridurre in forma prenex le seguenti formule

1) $R(x) \rightarrow (R(y) \rightarrow \exists x P(x,y))$
2) $\exists x P(x) \leftrightarrow \exists x Q(x)$
3) $\exists x \forall y R(x,y) \vee \forall x \exists y Q(x,y)$


Svolgo il primo
$\neg R(x) \vee (\neg R(y) \vee \exists x P(x,y))$
$\neg R(x) \vee \exists x (\neg R(y) \vee P(x,y))$
$\neg R(x) \vee \exists z (\neg R(y) \vee P(z,y))$
$\exists z (\neg R(x) \vee \neg R(y) \vee P(z,y))$


Svolgo il secondo
$(\exists x P(x) \rightarrow \exists x Q(x)) \wedge (\exists x Q(x) \rightarrow \exists x P(x)) $
$(\neg \exists x P(x) \vee \exists x Q(x)) \wedge (\neg \exists x Q(x) \vee \exists x P(x)) $
$(\forall x (\neg P(x)) \vee \exists y Q(y)) \wedge (\forall x ( \neg Q(x)) \vee \exists z P(z)) $
$\forall x (\neg P(x) \vee \exists y Q(y)) \wedge \forall x ( \neg Q(x) \vee \exists z P(z)) $
$\forall x ((\neg P(x) \vee \exists y Q(y)) \wedge ( \neg Q(x) \vee \exists z P(z))) $
$\forall x (\exists y (\neg P(x) \vee Q(y)) \wedge \exists z ( \neg Q(x) \vee P(z))) $
$\forall x \exists y \exists z ( (\neg P(x) \vee Q(y)) \wedge ( \neg Q(x) \vee P(z))) $

Svolgo il terzo
$\exists x \forall y R(x,y) \vee \forall z \exists w Q(z,w)$
$\exists x \forall y \forall z \exists w (R(x,y) \vee Q(z,w))$

Ho fatto molti errori? Grazie!

[xunil1987]

"perplesso":Ho fatto molti errori? Grazie!

Nessuno!

[perplesso1]

Thank you.