Help - Relational Algebra expressions

Given a column with some duplicated values, how does one go about pulling out a subset of that column with all the unique values in it?

E.g: Given the relation Serves with attributes [pizzeria_name, pizza_name, price], I'm interested in knowing the names of the pizzas whose prices are under $10 everywhere they are served.

I can do a selection to get pizzas under $10, and I can project the names into a column, but I have no idea how to get the unique names only.

EDIT: I think I might be retarded and the relational algebraic projection actually already takes care of this.

I've been banging my head against the wall, the table and the kitchen floor the whole day, and I need help.

Is there any alternative to using the select operator in order to filter out specific tuples that satisfy certain conditions?

Generally, if the conditions are given explicitly, select wouldn't be a problem, but I can't use it for cases where the conditions are implied/abstract (all names starting with "M" instead of Name="Mary", for example Actually that's a bad example since I imagine it's easily solvable with regex; so, say, all names which are longer than "John").

 Original problem

Given these three relations/tables:
Person

name	age	gender
Mary	16	female
Susan	19	female
Sal	32	male

Eats

name	pizza
Mary	cheese
Susan	cheese
Susan	mushroom
Sal	cheese
Sal	supreme
Sal	mushroom

Serves

pizzeria	pizza	price
Pizza Hut	cheese	9.75
Pizza Hut	mushroom	10.5
Straw Hat	supreme	12
Dominos	mushroom	11

Find all pizzerias that serve [b]every pizza eaten by people over 30[/b].

Problem is I don't know how to establish the "every" condition, and I can't perform a selection with the pizzas as conditions, since I don't know how many pizzas there are.

Hold on, I'm tinkering with this right now, actually. I'll let you know in about 10 minutes if I find out. This actually makes me curious too.

EDIT: Derp. I got stuck when I was working on the relationship. HERP DERP. FFFF- nvm. ; _; I'm a letdown . . . Sorry, Kalovale.

EDIT2: Actually, I remembered doing some sort of query on my project where I did a report, and it'll look up all weapons that are set at a specific rarity (1-15), but I don't think I had a query that enabled me to look up specific things that were above a specific amount. Ugh. If anybody here knows how to do that, I'd be interested in seeing too. -_-

I found a way to cheat at the problem, it's quite frustrating that I still can't come up with anything decent, though.

1/ find all pizzerias that serve at least one of the pizzas we want (Person \join_{age>"30"} Eats \join Serves), project the pizzeria-pizza relations
2/ self-join with new schemas (pizzeria, pizza1) and (pizzeria, pizza2) with condition (pizza1 != pizza2). As a result, get the relations of pizzerias that serve MORE THAN ONE pizza
* This way, we rule out the pizzerias that serve only one type of pizza, because its pizza1 will coincide with pizza2, inevitably

For this particular database, we only have 2 types of pizzas that people over 30 years old eat, so this works out (whatever passes the filter serves 2 types of pizza and thus "every" type). For other databases, we can easily find the number of pizzas that people over 30 years old eat, and keep recursing step 2 until we rule out all the ones that don't serve EVERY one of them.
Realistically, it works, it's just not a one-size-fits-all solution.