Max() in Domain Relational Calculus

Question

I was looking through my notes on domain relational calculus, and noticed an interesting result in a question about finding the most expensive pizza(s), given a pizza table with schema $\text{pizza}(\underline{id}, size)$. The first idea that came to me was:

$$\{id1\ |\ \exists size1, \forall id2, \forall size2 \ (\text{pizza}(id1, size1) \land \text{pizza}(id2, size2) \land size1 \ge size2)\}$$

i.e. A pizza which is at least at big as every other pizza is the most expensive. But the answer given was instead:

$$\{id1\ |\ \exists size1, \forall id2, \forall size2 \ (\text{pizza}(id1, size1) \land (\text{pizza}(id2, size2) \to size1 \ge size2))\}$$

The subtle change being that the last $\land$ was switched with a $\to$. I tried converting the if/then to $\lnot pizza(\ldots)\lor size1 \ge size2$ to get an intuitive idea on what exactly causes my former answer to be wrong, but can't seem to put my finger on it. Can anyone grok the differences between both expressions, and why the former isn't the answer? Appreciate it!