But what the sign says is either "no(food && drink)" or "no(food) && drink", depending on how you feel about precedence. The obvious implication in the first case is that either food or drink, or neither, but not both, is permissible; in the second, it's that drink is acceptable only when not also accompanied by food, but no other constraint is expressed with regard to either. If the intent was to express that neither food nor drink is permissible in any combination, the correct form, both logically and grammatically, would be "No food or drink".
