title: How to find all pizzerias that serve every pizza eaten by people over 30?
body: <p>I'm following the Stanford Database course and there's a question where we have <strong>Find all pizzerias that serve every pizza eaten by people over 30</strong> using Relational Algebra only.</p>
  
  <p>The problem consist of <a href="http://s3.amazonaws.com/dbclass-resources/docs/pizza.sql" rel="noreferrer">a small database with four relations:</a></p>
  
  <pre><code>Person(name, age, gender)       // name is a key
  Frequents(name, pizzeria)       // [name,pizzeria] is a key
  Eats(name, pizza)               // [name,pizza] is a key
  Serves(pizzeria, pizza, price)  // [pizzeria,pizza] is a key
  </code></pre>
  
  <p>I know how to find which pizza's people over 30 eat and make a cross-product of them, so I could check which pizzeria has both. </p>
  
  <p>I can make a list of all the pizzeria's that serve those pizza's, but I have no idea how to remove any pizzeria that only have one combination (like Dominos).</p>
  
  <pre><code>Chicago Pizza   cheese  cheese
  Chicago Pizza   cheese  supreme
  Chicago Pizza   supreme cheese
  Chicago Pizza   supreme supreme
  Dominos         cheese  cheese
  Dominos         cheese  supreme
  </code></pre>
  
  <p>The Q&amp;A forums tell us to use division and <a href="http://www.cs.arizona.edu/~mccann/research/divpresentation.pdf" rel="noreferrer">point us to several presentations.</a> While I get what the result of the action would be, I don't really understand how to translate the formula's into relational algebra syntax.</p>
  
  <p>Could anyone explain me what I'm missing, hopefully without giving the solution outright?</p>