Correcting my first order logic translations

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toshiba_me
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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.
[tex](\neg \exists x)(Barber(x) \wedge (\forall y)(Shaves(y,y) \Leftrightarrow Shaves(x,y)))[/tex]

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

3. White birds can fly.
[tex](\forall x)(Bird(x) \wedge White(x) \rightarrow Fly(x))[/tex]

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

Thanks for your help.

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

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