Prove the following statement:
(∀ x ∈ R) (∃ y ∈ R)[(-y x^2)]
Your proof should start with \Let x be an arbitrary real number. . . " and go on to produce a y in terms
of x which satisfies the desired property.

So I have no idea how to do this, I started with:

Let x in R be arbitrary.
We know x^2 ≥ 0
so, -y ≥ 0
dividing by -1 we get,
y ≤ 0 Therefore there exists a y for all x such that --y x^2

Is that a valid answer?

Question

Prove the following statement:
(∀ x ∈ R) (∃ y ∈ R)[(-y > x^2)]
Your proof should start with \Let x be an arbitrary real number. . . " and go on to produce a y in terms
of x which satisfies the desired property.

So I have no idea how to do this, I started with:

Let x  in R be arbitrary.
We know x^2 ≥ 0
so, -y  ≥ 0
dividing by -1 we get, 
y ≤ 0 Therefore there exists a y for all x such that --y > x^2

Is that a valid answer?

anonymous · Answer

is this algebra 3?

anonymous · Answer

i guess you could pick $y=-x^2-1$

anonymous · Answer

then it should be pretty clear that $-y>x^2$