predicates and quantifier problems

Let C(X0 be the statement "x has a cat", let D(x) be the statement "x has a dog" and let F(x) be the statement "x has a ferret". Express the statements in terms if the C(x),D(x), and F(x), quantifiers, and logical connectives. Let the domain be all student in class.

a. For each of the three animals, cats,dogs,and ferrets, there is a student in your class who has one of these animals as a pet.

my answer is:

$\displaystyle \exists x [C(x) \vee D(x) \vee F(x)] $

Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.

$\displaystyle \exists x(\neq P(x)) \wedge \forall x((x < 0) \rightarrow P(x)) $

my answer is:

$\displaystyle [\neg P(-5) \vee \neg P(-3) \vee \neg P(-1) \vee \neg P(1) \vee \neg P(3) \vee \neg P(5)] \wedge [P(5) \wedge P(3) \wedge P(1)] $