Need to convert following FOL expression into English
∀x [∃y father(y,x) ∧ ∃z mother(z,x)] → husband(y,z)
So far I think it says
Everybody has a father and mother such that father is the husband of the mother.
But wouldn't that y and z in the predicate husband are free variables. So could I say something like that.
And also, if I move the quantifiers into the leftside as follows would it be much suitable for my interpretation
∀x ∃y ∃z [[father(y,x) ∧ mother(z,x)] → husband(y,z)]
Yes, the problem with the first FOL expression is that it indeed has free variables y and z in the husband(y,z), so it is impossible to translate that into an English sentence, since if those variables are universally quantified you get a different sentence than if they are existentially quantified.
So, I think you are right to just assume there is an extra set of parentheses intended here, exactly as you propose.
But: your translation is not correct. The (second) FOL sentence says that any father of someone is the husband of any mother of that person. Which differs from your translation 'every has a father and mother such that the father is the husband of the mother' in the following ways:
In your translation, someone could have multiple fathers and/or mothers, but there would only have to be one father that is the husband of a mother ... so there could be other fathers who are not the husband of any mother at all
In your translation, everyone definitely has a father and a mother. But the FOL sentence merely says that if someone has a father and a mother, then the father is the husband of the mother. So: with the FOL sentence, you could have persons without any father or mother at all
Now I understand that both of those differences are unlikely to occur in reality: persons without a father and mother? Persons with multiple fathers or mothers? But, logic doesn't really care about that: the whole point of logic is that you need to express exactly those kinds of things, and what is not expressed, cannot be assumed in your translation.