I am given the proposition: $$\forall x \forall y \exists z\ (z = (x \cdot y))$$
It's not clear to me whether I am to interpret this as
For all
xand For ally, there exists azwhere(z = (x * y))is true
Where this is can be thought of as one node in set z being related to every node in sets x and y, equivalent to $\forall x \exists z \land \forall y \exists z$ ; a one-to-many relationship twice where z is the 'one' both times.
or if it should be interpreted as
For all
x, it will be the case that For ally, there exists azwhere(z = (x * y))is true
Where I guess an example could be "For every number, it will be true that for every number, there will be a number that when divided by 0 is equal to 0", but there doesn't seem to be a meaningful relationship between between the first universal quantifier and the second.