This translate in the logic predicate is true or not

Question

I found in a book , this phrase : There is a man who loves all women.

the logic predicate is : $\exists x(m(x)\wedge\forall y(w(y)\wedge love(x,y)))$ or not

Answer 1

Actually it is not. The problem is found in the part $\forall y(w(y)\wedge love(x,y))$, because that means that all people are women and loved by the man $x$. A proper formula would be the following:

$$\exists x(m(x)\wedge\forall y(w(y)\rightarrow love(x,y)))$$

In which case now it says that if $y$ is a woman, then $y$ is loved by $x$.