我已经完成了斯坦福大学的关系代数课程，并且很难理解其中一个问题，尽管我已经找到了答案。
这是模式：
/* Delete the tables if they already exist */
drop table if exists Person;
drop table if exists Frequents;
drop table if exists Eats;
drop table if exists Serves;
/* Create the schema for our tables */
create table Person(name text, age int, gender text);
create table Frequents(name text, pizzeria text);
create table Eats(name text, pizza text);
create table Serves(pizzeria text, pizza text, price decimal);
/* Populate the tables with our data */
insert into Person values('Amy', 16, 'female');
insert into Person values('Ben', 21, 'male');
insert into Person values('Cal', 33, 'male');
insert into Person values('Dan', 13, 'male');
insert into Person values('Eli', 45, 'male');
insert into Person values('Fay', 21, 'female');
insert into Person values('Gus', 24, 'male');
insert into Person values('Hil', 30, 'female');
insert into Person values('Ian', 18, 'male');
insert into Frequents values('Amy', 'Pizza Hut');
insert into Frequents values('Ben', 'Pizza Hut');
insert into Frequents values('Ben', 'Chicago Pizza');
insert into Frequents values('Cal', 'Straw Hat');
insert into Frequents values('Cal', 'New York Pizza');
insert into Frequents values('Dan', 'Straw Hat');
insert into Frequents values('Dan', 'New York Pizza');
insert into Frequents values('Eli', 'Straw Hat');
insert into Frequents values('Eli', 'Chicago Pizza');
insert into Frequents values('Fay', 'Dominos');
insert into Frequents values('Fay', 'Little Caesars');
insert into Frequents values('Gus', 'Chicago Pizza');
insert into Frequents values('Gus', 'Pizza Hut');
insert into Frequents values('Hil', 'Dominos');
insert into Frequents values('Hil', 'Straw Hat');
insert into Frequents values('Hil', 'Pizza Hut');
insert into Frequents values('Ian', 'New York Pizza');
insert into Frequents values('Ian', 'Straw Hat');
insert into Frequents values('Ian', 'Dominos');
insert into Eats values('Amy', 'pepperoni');
insert into Eats values('Amy', 'mushroom');
insert into Eats values('Ben', 'pepperoni');
insert into Eats values('Ben', 'cheese');
insert into Eats values('Cal', 'supreme');
insert into Eats values('Dan', 'pepperoni');
insert into Eats values('Dan', 'cheese');
insert into Eats values('Dan', 'sausage');
insert into Eats values('Dan', 'supreme');
insert into Eats values('Dan', 'mushroom');
insert into Eats values('Eli', 'supreme');
insert into Eats values('Eli', 'cheese');
insert into Eats values('Fay', 'mushroom');
insert into Eats values('Gus', 'mushroom');
insert into Eats values('Gus', 'supreme');
insert into Eats values('Gus', 'cheese');
insert into Eats values('Hil', 'supreme');
insert into Eats values('Hil', 'cheese');
insert into Eats values('Ian', 'supreme');
insert into Eats values('Ian', 'pepperoni');
insert into Serves values('Pizza Hut', 'pepperoni', 12);
insert into Serves values('Pizza Hut', 'sausage', 12);
insert into Serves values('Pizza Hut', 'cheese', 9);
insert into Serves values('Pizza Hut', 'supreme', 12);
insert into Serves values('Little Caesars', 'pepperoni', 9.75);
insert into Serves values('Little Caesars', 'sausage', 9.5);
insert into Serves values('Little Caesars', 'cheese', 7);
insert into Serves values('Little Caesars', 'mushroom', 9.25);
insert into Serves values('Dominos', 'cheese', 9.75);
insert into Serves values('Dominos', 'mushroom', 11);
insert into Serves values('Straw Hat', 'pepperoni', 8);
insert into Serves values('Straw Hat', 'cheese', 9.25);
insert into Serves values('Straw Hat', 'sausage', 9.75);
insert into Serves values('New York Pizza', 'pepperoni', 8);
insert into Serves values('New York Pizza', 'cheese', 7);
insert into Serves values('New York Pizza', 'supreme', 8.5);
insert into Serves values('Chicago Pizza', 'cheese', 7.75);
insert into Serves values('Chicago Pizza', 'supreme', 8.5);我正在努力解决问题6。问题如下：查找所有仅由24岁以下的人食用的披萨，或在所有送达地点的价格都低于10美元的披萨。
现在，我了解了查询。它基本上分为两个部分：
我什至理解答案，即（所有比萨饼和价格大于10美元的比萨饼之间的差异）和（人们所吃的所有比萨饼与24岁以上的人们所吃的所有比萨饼之间的差异）的联合
(\project_{pizza} (Serves) \diff \project_{pizza} (\select_{price>='10'} Serves))
\union
(\project_{pizza} (Eats) \diff \project_{pizza} (\select_{age>='24'} Person \join Eats))
但是，我不明白为什么相反的查询没有给出相同的答案，即（价格低于10美元的比萨饼）和（年龄小于24岁的人吃的比萨饼）的并集。
(\project_{pizza} (\select_{price<'10'} Serves))
\union
(\project_{pizza} (\select_{age<'24'} Person \join Eats))
为什么第二个查询给出的答案与第一个查询不同。据我说，他们俩都应该给出相同的答案。
所有答复表示赞赏。
您的第一个查询找到的披萨
不花费更多的$ 10的任何地方，或者是没吃过的任何24岁以上的人，
而您上一次查询时发现的比萨
销售低于$ 10的地方，或者是吃用一些低于24人。
对于在某些地方售价低于10美元而在其他地方售价高于10美元，或者被年龄在24岁以下且年龄更大的一些人食用的披萨，这些查询将给出不同的结果。
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