Max() in Domain Relational Calculus
For the first solution suppose, given  $id2$ and $size2$ which $\neg pizza(id2, size2)$ and $size1 &lt; size2$. Although, the first solution said $pizza(id1, size1)$ is not maximum (because it is not true for all $id2$ and $size2$), but it can be false. 
Because, if $(id1, size1)$ is the only member of the table, it is the maximum.
Therefore, the first solution have some fallacy.

To correct the case, you should mention that if $(id2,size2)$ is member of $pizza$ relation, then $size1 \geq size2$ and you can write this proposition as $pizza(id2, size2) \rightarrow size1 \geq size 2$.