Question

Help negating quantified logical expressions. Picture of problem will be attached

Answer 1

This is what I got
a:
∃x¬(x^2 + 2 ≥ 0) or ∃x(-x^2-2<0)

Answer 2

b.
∃x∀y¬(x ≥ y) or ∃x∀y(-x < -y)

Answer 3

c.
∃x∃y¬P(x,y) or ∃x∃yP(-x,-y)

Answer 4

d.
∀x∀y¬(3x+2y=0) or ∀x∀y(-3x-2y=0)

Answer 5

the reason I have the "or" in my answers is because I am not sure how to handle the negation of the stuff in parenthesis.

Answer 6

When you negate a statement, you're switching it to the opposite,

So the opposite of \(\rm x^2+2\ge0\) is \(\rm x^2+2\le0\).
If you think of it in terms of a number line, it might help.