To simplify the Boolean expression you provided:

$F = \left( A \cdot \overline{B} + \overline{C} \right) \; \text{XNOR} \; \left( (A \cdot \overline{B} \cdot C \cdot \overline{D}) + (B \cdot \overline{D}) \right)$

Let's break this down step by step:

1. First term: $A \cdot \overline{B} + \overline{C}$

   • This represents an OR between $A \cdot \overline{B}$ and $\overline{C}$.