## Describing Sets

### Describing Sets

There are two convenient ways to define sets. So far, our sets have been written out in **list** **notation**, meaning that each element is written in the set or is implied by a set pattern using "...".

We can also write sets using **predicate notation**, which uses a *variable* and a *description* to introduce the set. The general format of a set written in predicate notation looks like the following:

{VARIABLE | VARIABLE is DESCRIPTION}

Let's look at our old example containing the set of letters and write it out using list notation and predicate notation.

- Letters = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}
- Letters = {x | x is a letter of the English alphabet}
- This is read as "the set of x such that x is a letter of the English alphabet".

Here's another example using primary colors.

- P = {red, yellow, blue}
- P = {x | x is a primary color}
- This is read as "the set of x such that x is a primary color".

We say that two sets are **equivalent** iff they contain exactly the same elements. By definition, any set written in list notation is equivalent to the *same* set written in predicate notation.

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