1. The problem is to simplify the Boolean expression $ (xy)' + (x' + y') $. 2. Recall De Morgan's Law: $ (xy)' = x' + y' $. This law states that the complement of a product is the sum of the complements. 3. Substitute $ (xy)' $ with $ x' + y' $ in the expression: $$ (xy)' + (x' + y') = (x' + y') + (x' + y') $$ 4. Since $ (x' + y') + (x' + y') = x' + y' $ (idempotent law in Boolean algebra), the expression simplifies to: $$ x' + y' $$ 5. Therefore, the simplified form of the Boolean expression $ (xy)' + (x' + y') $ is $ x' + y' $.