Assume the existence of a database with the following relations: Ingredient (name, calories, cost, containsNuts) Recipe(name, ingredientName, amount) Menu(recipeName, season) which is used by a restaurant to manage its menu items. Assume that Recipe.ingredientName is a foreign key to Ingredient.name, and that Menu.recipeName is a foreign key to Recipe.name. Ingredi ent.containsNuts is a boolean, indicating whether the given ingredient contains nuts (e.g., PeantOil Assume all amounts are in the same unit (e.g., grams) Write relational algebra expressions for the following: (a) (3 points) List the names of all recipes on the menu for the Fall season (b) (3 points) List the names of all of the ingredients in Pizza (c) (3 points) List al of the recipes that are nut-free (d) (3 points) List all of the recipes on the Spring menu that contain nuts