First order logic to English statement? Assume
$A(x) = x$ is an American.
$D(y) = y$ is a dream.
$H(x,y) = x$ has $y$.

Then, Convert below first order logic to English statements :

*

*$∀x ∃y \left ( A(x)\rightarrow D(y) ∧ H(x,y) \right )$

I tried to translate this as "Every American has his own set of dreams".



*

*$∀x ∃y \left ( A(x) ∧ D(y) \rightarrow  H(x,y) \right )$

Not getting how is this pronounced ?
For this, I guess it is like "For all x if x is an American and there exists some y, such that y is a dream then x has y".


How much both of them are correct ?

What ∀x∃y(A(x)∧D(y)→H(x,y)) literally means in English, according to your given information is that for all Americans, there exists a dream y such that if every American x has at least one dream y, then they have their own dreams. In other words, every American with a dream sets has their own set of dreams.
