Set Definition by Predicate/Examples/Musical Mathematicians

Example of Set Definition by Predicate
Let $M$ denote the set of all the mathematicians in the world.

Let $I$ denote the set of all people who can play a musical instrument.

Let $S$ denote the set of all mathematicians who can play a musical instrument.

Then we can define $S$ as:
 * $S := \set {x: x \in M \text { and } x \in I}$

or as:


 * $S := \set {x \in M: x \in I}$