[Mathematical logic] prenex normal form and skolem normal form

[Nico]

Homework Statement

[Mathematical logic] convert the following equation into prenex normal form and skolem normal form.

Relevant Equations

(a) ~∃x∃y(~p(x) ∧ ∀z q(y, z) )


(b) ∀x ( p(x) ⇔ ∃y q(y, x) )


(c) ~(∀p(x)∧∀y∃zq(y, z)∧∀y∃z q(z, y))

The attached picture below is the note I solved halfway through.

Please tell me the entire process of getting to the correct answer.

 

[Mark44]

@Nico, we discourage the use of images that show work done, because they are usually illegible due to small image size or otherwise difficult to read.
Please show your work either as text or preferably, using LaTeX. There is a link to our tutorial at the lower left corner of the text entry pane.