Correcting my first order logic translations

[toshiba_me]

Homework Statement

Well the problem is: translate the following sentences in first order logic. I cannot verify whether they are correct or not. Maybe someone can point out my mistakes.

1. No barber shaves persons shaving themselves.
$$(\neg \exists x)(Barber(x) \wedge (\forall y)(Shaves(y,y) \Leftrightarrow Shaves(x,y)))$$

2. Any Barber shaves all the persons not shaving themselves.
$$(\forall x)(Barber(x) \wedge (\forall y) (\neg \Shaves(y,y) \Leftrightarrow Shaves(x,y)))$$

3. White birds can fly.
$$(\forall x)(Bird(x) \wedge White(x) \rightarrow Fly(x))$$

4. A bird is happy if all its children can fly.
$$(\forall x,y)(ChildOf(x, y) \wedge Fly(x) \rightarrow Bird(y) \wedge Happy(y))$$

Thanks for your help.

Please make corrections and suggestions whenever you do see fit. Excuse me for my english.

 

[lippyka]

Homework Equations The Attempt at a Solution 1. No barber shaves persons shaving themselves.(\neg \exists x)(Barber(x) \wedge (\forall y)(Shaves(y,y) \Leftrightarrow Shaves(x,y)))2. Any Barber shaves all the persons not shaving themselves.(\forall x)(Barber(x) \wedge (\forall y) (\neg Shaves(y,y) \Leftrightarrow Shaves(x,y)))3. White birds can fly.(\forall x)(Bird(x) \wedge White(x) \rightarrow Fly(x))4. A bird is happy if all its children can fly.(\forall x,y)(ChildOf(x, y) \wedge Fly(x) \rightarrow Bird(y) \wedge Happy(y))