Past exam of the computer science course of the University of Oxford / 2015 / Databases / 1 / c / ii

Take a unary database relation $R$ and the positive domain relational calculus queryFor the finite input $R=\{0\}$, every pair $(0,d)$ and $(d,0)$ belongs to $Q$, for every value $d$ in the ambient domain. On an infinite ambient domain the answer is infinite. Even if one compares only finite ambient domains, adding a fresh value $d$ changes the answer while leaving $R$ fixed, violating domain independence of a database query.

The logical disjunction leaves $y$ unrestricted in its first branch and $x$ unrestricted in its second branch. Thus both variables occur in relational atoms somewhere in the formula, yet database query safety still fails. No negation or implication symbol occurs.