The predicate $\mathrm{A}<15$ depends only on attribute $\mathrm{A}$.
Since $\mathrm{A}$ occurs only in $\mathrm{X}$, this condition can be applied directly to $\mathrm{X}$:
$\sigma_{\mathrm{A}<15}(\mathrm{X})$.
Similarly, $\mathrm{C}\geq10$ depends only on $\mathrm{Y}$:
$\sigma_{\mathrm{C}\geq10}(\mathrm{Y})$.
Therefore, both selections can be performed before the join:
$\boxed{\sigma_{\mathrm{A}<15}(\mathrm{X})\bowtie\sigma_{\mathrm{C}\geq10}(\mathrm{Y})}$.
This reduces the relations before the join while preserving the result.
B is not valid because $\mathrm{C}$ does not belong to $\mathrm{X}$.
C fails to enforce $\mathrm{C}\geq10$.
D changes a join query into a union and is not even union-compatible here.
Hence, the correct answer is A.
