Writing down propositions symbolically & state truth values.

Hey guys, I need help with a study question. "Write down the following propositions symbolically and state their values. Then write down the negation of each propositions."

a) There is a real number $\displaystyle x$ such that $\displaystyle x^2 - 3x + 2 = 0$.

*My Answer:* $\displaystyle \exists x \epsilon \mathbb{R}$ $\displaystyle (x^2 - 3x + 2 = 0)$ and this is **TRUE **for when $\displaystyle x=1$. The negation to this is $\displaystyle \forall x \epsilon \mathbb{R}$$\displaystyle (x^2 - 3x + 2 \neq 0)$

b) For every real number $\displaystyle x$ there is a real number $\displaystyle y$ such that $\displaystyle x=y^2$.

*My Answer:* $\displaystyle \forall x \epsilon \mathbb{R}$ $\displaystyle \exists y \epsilon \mathbb{R}$ $\displaystyle (x=y^2)$ and this is **FALSE **because not a single $\displaystyle y$ real value for $\displaystyle y^2$ can equal all real values of $\displaystyle x$. The negation to this is $\displaystyle \exists x \epsilon \mathbb{R}$ $\displaystyle \forall y \epsilon \mathbb{R}$ $\displaystyle (x \neq y^2)$

Are my answers OK? thanks