Could someone please help me with these predicate logic statements:

domain: all students in your class

C(x): "x has a cat"

D(x): "x has a dog"

F(x): "x has a ferret"

Some student in your class has a cat and a ferret, but not a dog.

$\displaystyle

\exists{x[C(x)\wedge}{F(x)\wedge}{\neg}{D(x)]}

$

No student in your class has a cat, a dog, and a ferret.

$\displaystyle

\forall{\neg}{[C(x)\wedge}{D(x)\wedge}{F(x)]}

$

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

$\displaystyle

\forall{x}\exists{x[C(x)\vee}{D(x)\vee}{F(x)]}

$

A little unsure about this one.

The next question:

P(x): "x is a duck"

Q(x): "x is one of my poultry"

R(x): "x is an officer"

S(x): "x is willing to waltz"

No ducks are willing to waltz.

$\displaystyle

\forall{x[P(x)\rightarrow}{\neg}{S(x)]}

$

No officers ever decline to waltz.

$\displaystyle

\forall{x[}{\neg}{R(x)\rightarrow}{\neg}{S(x)]}

$

All my poultry are ducks.

$\displaystyle

\forall{x[Q(x)\rightarrow}{P(x)]}

$

My poultry are not officers.

$\displaystyle

\forall{x[Q(x)\rightarrow}{\neg}{R(x)]}

$