leker

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 ex