Step 1: Understanding the behavior of XF$_3$ and YF$_3$.
- XF$_3$ is a Lewis acid, which means element X must have an incomplete octet or a strong tendency to accept electron pairs. This typically happens when the central atom has a higher oxidation state and can accept electron pairs. This is characteristic of sp$^3$ hybridized species.
- YF$_3$ acts as a Lewis base, which means element Y donates electron pairs. This occurs when element Y has lone pairs of electrons available for donation, and such atoms are typically sp$^3$ hybridized.
Step 2: Analyzing the hybridization of X and Y.
- For XF$_3$, X needs to have an oxidation state of +3, and its hybridization is sp$^3$ to accommodate three bonding pairs with fluorine atoms and leave an empty orbital for accepting electron pairs.
- For YF$_3$, Y needs to have lone pairs to act as a Lewis base. It will also be sp$^3$ hybridized as it needs to accommodate three bonding pairs and retain one lone pair, allowing it to donate electrons.
Step 3: Conclusion.
The hybridization of both X and Y in XF$_3$ and YF$_3$ is sp$^3$. Therefore, the correct answer is (3).