Transform a wff to a prenex normal form

Question

Could you help solve this problem. I need to convert the following wff to a PNF

∀x(L(x)->∃x M(x,y)) I do not understand how universal quantifier and existential quantifier on same variable operate. Scope of ∀x includes ∃x M(x,y) too.

Thanks to help

Can you more clearly state what you are asking? And format the question using mathjax. — siegehalver, Jun 10 '17 at 17:26

Wuestenfux · Accepted Answer · 2017-06-10T17:30:51.510

0

They are not working on the same variable. In $∀x(L(x)->∃x M(x,y))$, the outer variable $x$ is bounded to the all-quantifier. In $\exists x[M(x,y)]$, $x$ is bounded by the existential quantifier. You could rename it such as in $∀x(L(x)->∃z M(z,y))$. On the other hand, $y$ is a free variable.

edited Jun 10 '17 at 17:30

answered Jun 10 '17 at 17:25

Wuestenfux

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But, the scope of ∀x includes ∃xM(x,y), would that not be a problem while renaming? – Animesh Acharya Jun 10 '17 at 17:49

Transform a wff to a prenex normal form

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