Question

negate the following statement:
∃x∀y [y > x → ∃z (z^2 + 5z = y)]

Answer 1

∀x∃y [y < x → ∀z (z^2 + 5z ≠ y)] ?

do I also change y < x to y > x?

Answer 2

I think so, but you also need to negate the "implies" (->).

Answer 3

what is the negation of →?

Answer 4

"p -> q" is the same as "NOT p OR q"

Answer 5

i think p→q=not p or q

Answer 6

So you need to negate NOT p OR q, which should result in p AND NOT q.