X ∨ ¬(Y ∨ ¬(X ∧ Y)).

To simplify the given expression \( X \lor \neg(Y \lor \neg(X \land Y)) \), we can use De Morgan's laws and distribution.

First, let's apply De Morgan's law to the inner part of the expression:

\( \neg(X \land Y) = \neg X \lor \neg Y \)

Now, substitute this back into the original expression:

\( X \lor \neg(Y \lor (\neg X \lor \neg Y)) \)

Using De Morgan's law again:

\( X \lor \neg(Y \lor \neg X \lor \neg Y) \)

Since \( Y \lor \neg Y \) is always true, we can simplify further:

\( X \lor \neg(\text{true} \lor \neg X) \)

Now, simplify this expression:

\( X \lor \neg(\text{true}) \)

Finally, we simplify to get the final answer:

\( X \lor \text{false} \)

Therefore, the simplified expression is simply \( X \).