# Correcting my first order logic translations

• toshiba_me
In summary, the problem is to translate sentences into first-order logic. The first sentence states that no barber shaves a person who is shaving themselves. The second sentence states that any barber shaves all persons who are not shaving themselves. The third sentence states that white birds are capable of flying. The last sentence states that a bird is happy if all its children can fly. Corrections and suggestions are welcome and the person apologizes for any mistakes in their English.

## 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.
$$(\forall x,y)(ChildOf(x, y) \wedge Fly(x) \rightarrow Bird(y) \wedge Happy(y))$$